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This paper concerns the regularity and uniqueness of 3D compressible micropolar fluids in the whole space R 3 . We first establish some new Lp gradient estimates of the solutions for the system, then by virtue of the "div-rot" decomposition technique, the key estimates ‖ ∇ u ‖ L 3 and ‖ ∇ w ‖ L 3 are obtained. As a result, the existence and uniqueness of global solutions belonging to a new class of functions are obtained, provided the initial energy is suitable small. It is worth noting that compared with the existing results, this paper has lower regularity of initial data. [ABSTRACT FROM AUTHOR]

The paper interprets the cubic nonlinear Schrödinger equation as a Hamiltonian system with infinite dimensional phase space. There exists a Gibbs measure which is invariant under the flow associated with the canonical equations of motion. The logarithmic Sobolev and concentration of measure inequalities hold for the Gibbs measures, and here are extended to the k-point correlation function and distributions of related empirical measures. By Hasimoto's theorem, the nonlinear Schrödinger equation gives a Lax pair of coupled ordinary differential equations for which the solutions give a system of moving frames. The paper studies the evolution of the measure induced on the moving frames by the Gibbs measure; the results are illustrated by numerical simulations. The paper contains quantitative estimates with well-controlled constants on the rate of convergence of the empirical distribution in Wasserstein metric. [ABSTRACT FROM AUTHOR]

On the one hand, the primitive three-dimensional viscous equations for large-scale ocean and atmosphere dynamics are commonly used in weather and climate predictions. On the other hand, ever since the middle of the last century, it has been widely recognized that the climate variability exhibits long-time memory. In this paper, we first prove the global existence of weak solutions to the primitive equations of large-scale ocean and atmosphere dynamics with Caputo fractional time derivatives. Then we establish the existence of an absorbing set, which is positively invariant. Finally, an attractor (strictly speaking, the minimal attracting set containing all the limiting dynamics) is constructed for the time fractional primitive equations, which means that the present state of a system may have long-time influences on the states in far future. However, there was no work on the long-time behavior of the time fractional primitive equations and we fill this gap in this paper. [ABSTRACT FROM AUTHOR]

In this paper we present a new exact solution that represents a Pollard-like, three-dimensional, nonlinear internal wave propagating on a non-uniform zonal current in a nonhydrostatic ocean model. The solution is presented in Lagrangian coordinates, and in the process we derive a dispersion relation for the internal wave which is subjected to a perturbative analysis which reveals the existence of two distinct modes of wave motion. [ABSTRACT FROM AUTHOR]

In this paper, we consider a random one-dimensional Schrödinger operator H ω on the half line which has, as its potential term, Gaussian white noise multiplied by a decaying factor. Although the potential term is not an ordinary function, but a distribution, it is possible to realize H ω as a symmetric operator in L2([0, ∞); dt) as was pointed out by the present author [Minami, Lect. Notes Math. 1299, 298 (1986)], and it will be shown that H ω is actually self-adjoint with probability one. When the white noise in H ω is replaced by random functions of a specific type, [Kotani and Ushiroya, Commun. Math. Phys. 115, 247 (1988)] made a precise analysis of the positive part of the spectrum. According to them, if the decaying factor is not square integrable, the positive part of the spectrum typically consists of singular continuous and dense pure-point parts, which are separated by a threshold number. On the other hand, the positive part of the spectrum is purely absolutely continuous when the decaying factor is square integrable. In this work, we shall focus on the case of square integrable decaying factor, and prove the absolute continuity of the positive part of the spectrum of H ω . We shall further prove that the negative part of the spectrum of H ω is discrete, with no accumulation points other than 0. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the affine ageing algebra a g e ̂ (1) , which is a central extension of the loop algebra of the one-spatial ageing algebra a g e (1). Certain Verma-type modules including Verma modules and imaginary Verma modules of a g e ̂ (1) are studied. Particularly, the simplicity of these modules are characterized and their irreducible quotient modules are determined. We also study the restricted modules of a g e ̂ (1) which are also the modules of the affine vertex algebra arising from the one-spatial ageing algebra a g e (1). We present certain constructions of simple restricted a g e ̂ (1) -modules and an explicit such example of simple restricted module via the Whittaker module of a g e ̂ (1) is given. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a family of functors denoted as F b , which act on algebraic D-modules and produce modules over N = 2 superconformal algebras. We demonstrate that these functors preserve irreducibility for all values of b, except for explicitly outlined cases. Moreover, we establish the necessary and sufficient conditions for determining the natural isomorphism between two such functors. Our constructed functors recover specific irreducible modules over N = 2 superconformal algebras, including intermediate series and U (h) -free modules. Additionally, we show that our constructed functors yield several new irreducible modules for N = 2 superconformal algebras. [ABSTRACT FROM AUTHOR]

In this paper, we consider a semilinear Bresse system in one dimensional bounded non homogeneous medium. We investigate stability issues for such a problem with a nonlinear damping acting in all three wave equations. We prove, firstly, the existence and uniqueness of the solutions by using the nonlinear semigroup method. Afterwords, we establish an uniform decay rates of the energy for these solutions without considering any restriction on the coefficients as well as the equality of the wave propagation speeds. Some techniques of the microlocal analysis theory are used in order to reach the desired asymptotics. [ABSTRACT FROM AUTHOR]

In this paper, we are concerned with a Kirchhoff-Choquard type equation with L2-prescribed mass. Under different cases of the potential, we prove the existence of normalized ground state solutions to this equation. To obtain the boundedness from below of the energy functional and the compactness of the minimizing sequence, we apply the Gagliardo-Nirenberg inequality with the Riesz potential and the relationship between the different minimal energies corresponding to different mass. We also extend the results to the fractional Kirchhoff-Choquard type equation. [ABSTRACT FROM AUTHOR]

In this paper, we consider the exact solutions of the complex cubic-quintic Ginzburg–Landau equation. By investigating the dynamical behavior of solutions of the corresponding traveling wave system of this PDE, we derive exact explicit parametric representations of the periodic wave solutions under given parameter conditions. [ABSTRACT FROM AUTHOR]

This paper is concerned with the vacuum free boundary problem of the 1D shallow water equations coupled with the Poisson equation. We establish the local-in-time well-posedness of classical solutions to this system, and the solutions possess higher-order regularity all the way to the vacuum free boundary, though the density degenerates near the vacuum boundary. To deal with the force term generated by the Poisson equation, we make use of the structure of the momentum equation formulated in a fixed domain by the Lagrangian coordinates. The proof is built on some higher-order weighted energy functionals and weighted embeddings corresponding to the degeneracy near the initial vacuum boundary. [ABSTRACT FROM AUTHOR]

A 2006 conjecture of Antunes and Freitas is addressed connecting the scaling-invariant polygonal isoperimetric and principal frequency deficits for triangles. This yields a quantitative polygonal Faber–Krahn inequality for triangles with an explicit constant. Furthermore, a problem mentioned in the 1951 book "Isoperimetric Inequalities In Mathematical Physics" by Pólya and Szegö is addressed: a formula is given for the principal frequency of a triangle. Moreover, a space of polygons is constructed for the classical Pólya and Szegö problem: in 1947, Pólya proved that if n = 3, 4 the regular polygon Pn minimizes the principal frequency of an n-gon with given area α > 0 and suggested that the same holds when n ≥ 5. In 1951, Pólya and Szegö discussed the possibility of counterexamples. This paper constructs explicit (2n − 4)–dimensional polygonal manifolds M (n , α) and proves the existence of a computable N ≥ 5 such that for all n ≥ N, the admissible n-gons are given via M (n , α) and there exists an explicit set A n (α) ⊂ M (n , α) such that Pn has the smallest principal frequency among n-gons in A n (α). Inter-alia when n ≥ 3, a formula is proved for the principal frequency of a convex P ∈ M (n , α) in terms of an equilateral n-gon with the same area; and, the set of equilateral polygons is proved to be an (n − 3)–dimensional submanifold of the (2n − 4)–dimensional manifold M (n , α) near Pn. The techniques involve a partial symmetrization, tensor calculus, the spectral theory of circulant matrices, and W2,p/BMO estimates. Last, an application is given in the context of electron bubbles. [ABSTRACT FROM AUTHOR]

In this paper, we focus on the global well-posedness of solutions to three-dimensional incompressible Boussinesq equations with temperature-dependent viscosity under the smallness assumption of initial velocity fields u0 in the critical space B ̇ 3 , 1 0 . The key ingredients here lie in the decomposition of the velocity fields and the regularity theory of the Stokes system, which are crucial to get rid of the smallness restricition of the initial temperature θ0. In addition, we mention that the improved decay estimates in time is also necessary. [ABSTRACT FROM AUTHOR]

The current paper aims to explore the three-dimensional axisymmetric viscous and resistive magnetohydrodynamic system. This article is concerned with two outcomes, in the first result we prove the global existence of a unique solution for this system under initial data lying in the Sobolev spaces Hs × Hs−2 with s > 5 2 , furthermore, we obtain uniform estimates with respect to the viscosity. The second outcome shows that the viscous and resistive solutions ( v μ , b μ ) μ > 0 strongly converge to the non-viscous one (v, b). This convergence is performed in the space L ∞ ( R + , H s − 2 × H s − 2 ) , also we obtain that the rate of convergence is (μt). [ABSTRACT FROM AUTHOR]

In this paper, for a given conservative solution, we introduce a set of auxiliary variables tailored to this particular solution, and prove that these variables satisfy a particular semilinear system having unique solutions. In turn, we get the uniqueness of the conservative solution in the original variables. [ABSTRACT FROM AUTHOR]

Recently, Ludewig and Thiang introduced a notion of a uniformly localized Wannier basis with localization centers in an arbitrary uniformly discrete subset D in a complete Riemannian manifold X. They show that, under certain geometric conditions on X, the class of the orthogonal projection onto the span of such a Wannier basis in the K-theory of the Roe algebra C*(X) is trivial. In this paper, we clarify the geometric conditions on X, which guarantee triviality of the K-theory class of any Wannier projection. We show that this property is equivalent to triviality of the unit of the uniform Roe algebra of D in the K-theory of its Roe algebra, and provide a geometric criterion for that. As a consequence, we prove triviality of the K-theory class of any Wannier projection on a connected proper measure space X of bounded geometry with a uniformly discrete set of localization centers. [ABSTRACT FROM AUTHOR]

We investigate Gaussian Laplacian eigenfunctions (Arithmetic Random Waves) on the three-dimensional standard flat torus, in particular the asymptotic distribution of the nodal intersection length against a fixed regular reference surface. Expectation and variance have been addressed by Maffucci [Ann. Henri Poincaré 20(11), 3651–3691 (2019)] who found that the expected length is proportional to the square root of the eigenvalue times the area of the surface, while the asymptotic variance only depends on the geometry of the surface, the projected lattice points being equidistributed on the two-dimensional unit sphere in the high-energy limit. He also noticed that there are "special" surfaces, so-called static, for which the variance is of smaller order; however he did not prescribe the precise asymptotic law in this case. In this paper, we study second order fluctuations of the nodal intersection length. Our first main result is a Central Limit Theorem for "generic" surfaces, while for static ones, a sphere or a hemisphere e.g., our main results are a non-Central Limit Theorem and a precise asymptotic law for the variance of the nodal intersection length, conditioned on the existence of so-called well-separated sequences of Laplacian eigenvalues. It turns out that, in this regime, the nodal area investigated by Cammarota [Trans. Am. Math. Soc. 372(5), 3539–3564 (2019)] is asymptotically fully correlated with the length of the nodal intersections against any sphere. The main ingredients for our proofs are the Kac-Rice formula for moments, the chaotic decomposition for square integrable functionals of Gaussian fields, and some arithmetic estimates that may be of independent interest. [ABSTRACT FROM AUTHOR]

It is known that the Lyapunov exponent for multifrequency analytic cocycles is weak-Hölder continuous in cocycle for certain Diophantine frequencies, and that this implies certain regularity of the integrated density of states in energy for Jacobi operators. In this paper, we establish the pointwise modulus of continuity in both cocycle and frequency and obtain analogous regularity of the integrated density of states in energy, potential, and frequency. [ABSTRACT FROM AUTHOR]

This paper examines the large time behavior of solutions to the 3D Hall-magnetohydrodynamic equations with horizontal dissipation. As preparations we establish the global well-posedness of solutions and their global explicitly uniform upper bounds for Hk (k ≥ 1) to this system with initial data small in H2. Furthermore, if the initial data also belongs to homogeneous negative Besov spaces, we prove the optimal decay rates of the aforementioned global solutions and their higher order derivatives. [ABSTRACT FROM AUTHOR]

In this paper, using the linking theorem and variational methods, we establish the existence of at least one positive solution for a class of fractional Hamiltonian-type elliptic systems with exponential critical growth in R. [ABSTRACT FROM AUTHOR]

The paper develops a finite-time quantum state reduction framework via the use of Lévy random bridges (LRBs) that can be understood as Doob h-transformations on Lévy processes. Building upon the non-anticipative semimartingale representation of LRBs, we propose a family of energy-driven stochastic Schrödinger equations that go beyond the purely-continuous Brownian motion setup, and enter the scope of quantum systems involving discontinuities and heavy-tails. In doing so, we allow collapse dynamics to be governed intrinsically by the Markovian statistics of LRBs. The framework can host progressively convoluted stochastic state reduction dynamics in a tractable way and encapsulates jump-diffusion Schrödinger evolutions by use of the Lévy-Itô decomposition. Our construct motivates the usage of more general Markov processes and Doob h-transformations in producing consistent wave function collapse dynamics in finite-time. [ABSTRACT FROM AUTHOR]

The notion of O -operator is a generalization of the Rota–Baxter operator in the presence of a bimodule over an associative algebra. A compatible O -operator is a pair consisting of two O -operators satisfying a compatibility relation. A compatible O -operator algebra is an algebra together with a bimodule and a compatible O -operator. In this paper, we construct a graded Lie algebra and an L∞-algebra that respectively characterize compatible O -operators and compatible O -operator algebras as Maurer–Cartan elements. Using these characterizations, we define cohomology of these structures and as applications, we study formal deformations of compatible O -operators and compatible O -operator algebras. Finally, we consider a brief cohomological study of compatible dendriform algebras and find their relationship with the cohomology of compatible associative algebras and compatible O -operators. [ABSTRACT FROM AUTHOR]

In this paper, we propose a new four-component Camassa–Holm-type system. The Lax pair and infinitely many conservation laws of this system are constructed. Bi-Hamiltonian structures and N-peakon solutions of some prototypical equations in this system are considered. In particular, the "W/M"-shape peakon solutions are obtained. [ABSTRACT FROM AUTHOR]

In this paper, we study a class of Kirchhoff type logarithmic Schrödinger equations involving the critical or supercritical Sobolev exponent. Such problems cannot be studied by applying variational methods in a standard way, because the nonlinearities do not satisfy the Ambrosetti-Rabinowitz condition and change sign. Moreover, the appearance of the logarithmic term makes the associated energy functional lose differentiable in the sense of Gateaux. By analyzing the structure of the Nehari manifold and developing some analysis techniques, the above obstacles are overcome in subtle ways and several existence result are obtained. Furthermore, we investigate the regularity, the monotonicity, and the symmetric properties of the solutions via the iterative technique and the moving plane method. [ABSTRACT FROM AUTHOR]

In this paper, new symmetry reductions and similarity solutions for Burgers equation with moving boundary are obtained by means of Lie's method of infinitesimal transformation groups, for a linearly moving boundary as well as a parabolically moving boundary. By using discrete symmetries, new analytical solutions for the problem under consideration are presented, for two cases of the moving boundary: one moving with constant velocity and another one rapidly oscillating. [ABSTRACT FROM AUTHOR]

In this paper, we consider the convergence rates for the 2D stationary and non-stationary Navier–Stokes Equations over highly oscillating periodic bumpy John domains with C2 regularity in some neighborhood of the boundary point (0,0). For the stationary case, using the variational equation satisfied by the solution and the correctors for the bumpy John domains obtained by Higaki and Zhuge [Arch. Ration. Mech. Anal. 247(4), 66 (2023)] after correcting the values on the inflow/outflow boundaries ({0} ∪ {1}) × (0, 1), we can obtain an O(ɛ3/2) approximation in L2 for the velocity and an O(ɛ3/2) convergence rates in L2 approximated by the so called Navier's wall laws, which generalized the results obtained by Jäger and Mikelić [J. Differ. Equations 170(1), 96–122 (2001)]. Moreover, for the non-stationary case, using the energy method, we can obtain an O(ɛ3/2 + exp(−Ct)) convergence rate for the velocity in L x 2 . [ABSTRACT FROM AUTHOR]

We investigate the Robin eigenvalue problem for the Laplacian with negative boundary parameter on quadrilateral domains of fixed area. In this paper, we prove that the square is a local maximiser of the first eigenvalue with respect to the Hausdorff metric. We also provide asymptotic results relating to the optimality of the square for extreme values of the Robin parameter. [ABSTRACT FROM AUTHOR]

This paper analyses robustness of pullback and exponential pullback attractors for the non-autonomous thermoelastic plate with p-Laplacian under the Coleman–Gurtin heat theory derived recently by Fatori et al. [J. Diff. Equ. 259, 4831–4862 (2015)]. Moreover, the existence of pullback attractors in the natural space energy with finite dimensionality is proved together with its upper semicontinuity and continuity with respect to the damped parameter α ∈ [0, 1]. Finally, we prove that the related process has a pullback exponential attractor M e x p α and its Hölder continuity on α ∈ [0, 1]. In particular, when the non-autonomous dynamical system degenerates to an autonomous one, the family of robust pullback and exponential pullback attractors become a robust global attractor and a robust exponential attractor, respectively, so the results of the paper deepen and extend those in Fatori et al. [J. Diff. Equ. 259, 4831–4862 (2015)]. [ABSTRACT FROM AUTHOR]

In the present paper, we consider two dimensional completely resonant, derivative, quintic nonlinear beam equations with reversible structure. Because of this reversible system without external parameters or potentials, Birkhoff normal form reduction is necessary before applying Kolmogorov–Arnold–Moser (KAM) theorem. As application of KAM theorem, the existence of partially hyperbolic, small amplitude, quasi-periodic solutions of the reversible system is proved in this paper. [ABSTRACT FROM AUTHOR]

In a recent series of papers new exact analytical solutions of the Einstein equations representing interior spacetimes sourced by stationary rigidly rotating cylinders of different kinds of fluids have been displayed, [Phys. Rev. D 104, 064040 (2021); J. Math. Phys. 64, 022501 (2023); J. Math. Phys. 64, 032501 (2023); J. Math. Phys. 64, 042501 (2023); and J. Math. Phys. 64, 052502 (2023)]. This work is currently being extended to the cases of differentially rotating irrotational fluids. The results are presented in a new series of papers considering in turn the same three anisotropic pressure cases, as well as a perfect fluid source. Here, the perfect fluid case is considered, and different classes are identified as directly issuing from the field equations. Among them, an explicit analytical set of solutions is selected as displaying perfect fluid spacetimes. Its mathematical and physical properties are analyzed. Its matching to an exterior Lewis-Weyl vacuum and the conditions for avoiding an angular deficit are discussed. [ABSTRACT FROM AUTHOR]

This article belongs to a series where the influence of anisotropic pressure on gravitational properties of rigidly rotating fluids is studied using new exact solutions of GR constructed for the purpose. For mathematical simplification, stationarity and cylindrical symmetry implying three Killing vectors are considered. Moreover, two pressure components are set to vanish in turn. In Papers I and II, the pressure is axially directed, while it is azimuthal in Paper III. In present paper (Paper IV), a radially directed pressure is considered. Since a generic differential equation, split into three parts, emerges from field equations, three different classes of solutions can be considered. Two could only be partially integrated. The other one, which is fully integrated, yields a set of solutions with a negative pressure. Physical processes where a negative pressure is encountered are depicted and give a rather solid foundation to this class of solutions. Moreover, these fully integrated solutions satisfy the axisymmetry condition, while they do not verify the so-called "regularity condition." However, since their Kretschmann scalar does not diverge on the axis, this feature must be considered as reporting a mere coordinate singularity. Finally, the matching of these solutions to an exterior appropriate vacuum enforces other constraints on the two constant parameters defining each solution in the class. The results displayed here deserve to be interpreted in light of those depicted in the other four papers in the series. [ABSTRACT FROM AUTHOR]

This paper is the second in a series devoted to the study of spacetimes sourced by a stationary cylinder of fluid rigidly rotating around its symmetry axis and exhibiting an anisotropic pressure by using new exact interior solutions of general relativity. The configurations have been specialized to three different cases where the pressure is, in turn, directed alongside each principal stress. The two first articles in the series display the analysis of the axial pressure case. Indeed, the first axial class published in Paper I is merely a special case. It is recalled here and its properties are revised and supplemented. Moreover, a fully general method aiming at constructing different classes of such solutions is displayed. This method described in Paper II represents a key result of this work. It is exemplified and applied to two new classes of solutions depending on a single constant parameter. One of them, denoted Class A, is shown to verify every condition needing to be satisfied by a fully achieved set of exact solutions: axisymmetry and, when appropriate, regularity conditions; matching to an exterior vacuum; proper metric signature; and weak and strong energy conditions. Other properties and general rules are exhibited, some shedding light on rather longstanding issues. Astrophysical and physical applications are suggested. [ABSTRACT FROM AUTHOR]

Cholera is a global epidemic infectious disease that seriously endangers human life. It is disturbed by random factors in the process of transmission. Therefore, in this paper, a class of stochastic SIRB cholera model with Ornstein–Uhlenbeck process is established. On the basis of verifying that the model exists a unique global solution to any initial value, a sufficient criterion for the existence of a stationary distribution of the positive solution of the random model is established by constructing an appropriate random Lyapunov function. Furthermore, under the same condition that there is a stationary distribution, the specific expression of the probability density function of the random model around the positive equilibrium point is calculated. Finally, the theoretical results are verified by numerical model. [ABSTRACT FROM AUTHOR]

The probability density is a fundamental quantity for characterizing diffusion processes. However, it is seldom known except in a few renowned cases, including Brownian motion and the Ornstein–Uhlenbeck process and their bridges, geometric Brownian motion, Brownian excursion, or Bessel processes. In this paper, we utilize Girsanov's theorem, along with a variation of the method of images, to derive the exact expression of the probability density for diffusions that have one entrance boundary. Our analysis encompasses numerous families of conditioned diffusions, including the Taboo process and Brownian motion conditioned on its growth behavior, as well as the drifted Brownian meander and generalized Brownian excursion. [ABSTRACT FROM AUTHOR]

Scanning the whole writing, we discuss a stochastic cooperative species system with distributed delays under the influences of Ornstein–Uhlenbeck process of mean regression. We successfully obtain the existence and uniqueness of positive solutions for stochastic system at first. Secondly, by studying the Lyapunov function, we present the existence of the stationary distribution of the system. We are relatively familiar with the understanding of the density function of random systems. This paper also gives the expression of the density function of the random system near the unique positive equilibrium. In addition, the asymptotic properties of the p-moment boundedness and solution of the stochastic population system are also studied. In particular, we use numerical simulation to verify the theoretical results in the last section. [ABSTRACT FROM AUTHOR]

The problem of computing the rate of diffusion-aided activated barrier crossings between metastable states is one of broad relevance in physical sciences. The transition path formalism aims to compute the rate of these events by analysing the statistical properties of the transition path between the two metastable regions concerned. In this paper, we show that the transition path process is a unique solution to an associated stochastic differential equation, with a discontinuous and singular drift term. The singularity arises from a local time contribution, which accounts for the fluctuations at the boundaries of the metastable regions. The presence of fluctuations at the local time scale calls for an excursion theoretic consideration of barrier crossing events. We show that the rate of such events, as computed from excursion theory, factorizes into a local time term and an excursion measure term, which bears empirical similarity to the transition state theory rate expression. Since excursion theory makes no assumption about the presence of a transition state in the potential energy landscape, the mathematical structure underlying this factorization ought to be general. We hence expect excursion theory (and local times) to provide some physical and mathematical insights in generic barrier crossing problems. [ABSTRACT FROM AUTHOR]

In this paper, pointwise preimage pressures for (non-invertible) continuous maps on any subset (not necessarily compact or invariant) are introduced via Carathéodory-Pesin construction. A variational inequality for preimage pressure of saturated sets is then obtained. In particular, we prove that the preimage pressure of the set of generic points for an ergodic measure equals the metric preimage pressure of the measure, which extends Bowen's theorem to preimage pressure. We also use the thermodynamic formalism of preimage pressure to obtain some estimates on Birkhoff level sets. [ABSTRACT FROM AUTHOR]

In this paper, we consider a reaction-diffusion cholera model with hyperinfectious vibrios and spatio-temporal delay. In the model, it is assumed that cholera has a fixed latent period and the latent individuals can diffuse, and a non-local term is incorporated to describe the mobility of individuals during the latent period. It is shown that the existence and nonexistence of traveling wave solutions are fully determined by the basic reproduction number R 0 and the critical wave speed c*. Firstly, when R 0 > 1 and the wave speed c > c*, the existence of strong traveling waves is obtained by using Schauder's fixed point theorem and Lyapunov functional approach. By employing a limiting argument, the existence of strong traveling waves is established when R 0 > 1 and c = c*. Next, when R 0 ≤ 1 , the nonexistence of traveling wave solutions is established by contradiction. Besides, when R 0 > 1 and c < c*, the nonexistence of traveling wave solutions is obtained by means of two-sided Laplace transform. This indicates that c* is indeed the minimal wave speed. Numerical simulations are carried out to illustrate the theoretical results. [ABSTRACT FROM AUTHOR]

This paper deals with the limiting dynamics of stochastic complex Ginzburg–Landau lattice systems with long-range interactions driven by nonlinear noise in a weighted space L 2 (Ω , l η 2 ). We first consider the well-posedness of solutions for considered stochastic systems in the weighted space and then establish the existence and uniqueness of weak pullback mean random attractor in the weighted space. [ABSTRACT FROM AUTHOR]

In this paper we consider n coupled Schrödinger equations − d 2 y d t 2 + u (ω t) y = E y , y ∈ R n , where E = diag ( λ 1 2 , ... , λ n 2 ) is a diagonal matrix, u(ωt) is a real analytic quasi-periodic symmetric matrix. If the basic frequencies ω = (1, α), where α is irrational, it is proved that for most of sufficiently large λj, j = 1, ..., n, all the solutions of n coupled Schrödinger equations are bounded. Furthermore, if the basic frequencies satisfy that 0 ≤ β(α) < r, where β (α) = lim sup n → ∞ ln q n + 1 q n , qn is the sequence of denominations of the best rational approximations for α ∈ R \ Q , r is the initial analytic radius, we obtain the existence of n pairs of conjugate quasi-periodic solutions for most of sufficiently large λj, j = 1, ..., n. [ABSTRACT FROM AUTHOR]

In a previous work, we established perturbative renormalizability to all orders of the massive ϕ 4 4 -theory on a half-space also called the semi-infinite massive ϕ 4 4 -theory. Five counter-terms which are functions depending on the position in the space, were needed to make the theory finite. The aim of the present paper is to establish that for a particular choice of the renormalization conditions the effective action consists of a part which is independent of the boundary conditions (Dirichlet, Neumann and Robin) plus a boundary term in the case of the Robin and Neumann boundary conditions. The key idea of our method is the decomposition of the correlators into a bulk part, which is defined as the scalar field model on the full space R 4 with a quartic interaction restricted to the half-space, plus a remainder which we call "the surface part." We analyse this surface part and establish perturbatively that the ϕ 4 4 theory in R + × R 3 is made finite by adding the bulk counter-terms and two additional counter-terms to the bare interaction in the case of Robin and Neumann boundary conditions. These surface counter-terms are position independent and are proportional to ∫Sϕ2 and ∫Sϕ∂nϕ. For Dirichlet boundary conditions, we prove that no surface counter-terms are needed and the bulk counter-terms are sufficient to renormalize the connected amputated (Dirichlet) Schwinger functions. A key technical novelty as compared to our previous work is a proof that the power counting of the surface part of the correlators is better by one scaling dimension than their bulk counterparts. [ABSTRACT FROM AUTHOR]

In this paper, we establish the existence of small-amplitude unique solutions near the Maxwellian for the Fokker–Planck–Boltzmann equation in a finite channel with specular reflection boundary conditions. The solution space we consider is denoted as L k ̄ 1 L T ∞ L x 1 , v 2 , introduced in Duan et al. [Commun. Pure Appl. Math. 74(5), 932–1020 (2021)]. In addition, we investigate the long-time behavior of solutions for both hard and soft potentials. [ABSTRACT FROM AUTHOR]

In this paper, we establish a Feynman–Kac formula for the stochastic parabolic Anderson model with Gaussian potential in space and fractional white noise in time with Hurst parameter H > 1/2. We obtain the necesscary and suffcient condition for the integrability of the Gaussian potential and the exponential integrability of the solution which is defined by Feynman–Kac formula. By the smoothing of the fractional white noise and techniques from Malliavin calculus, we prove that the Feynman–Kac representation is a mild solution of the stochastic parabolic Anderson equation. [ABSTRACT FROM AUTHOR]

This paper considers the global well-posedness of two-dimensional Klein–Gordon equations with exponential nonlinearity. By employing the potential well method, we conduct a comprehensive study on the global existence and finite time blowup of solutions by the requirement of the initial energy at three different initial energy levels. [ABSTRACT FROM AUTHOR]

In this paper, we investigate the global well-posedness and stability of steady supersonic Euler flows in a quasi-one-dimensional convergent nozzle. First, we show that there exists a critical nozzle length L1, the global well-posedness of steady supersonic flows can be obtained and the explicit solution is given as long as the nozzle length L < L1. Then we prove the global stability of steady supersonic flows under small perturbations of initial-boundary values by wave decomposition. [ABSTRACT FROM AUTHOR]

The purpose of this article is to study the correspondence between 3d-gravity and the Chern–Simons field theory from the perspective of geometric mechanics, specifically in the case where the structure group is the general affine group. To accomplish this, the paper discusses a variational problem of the Chern–Simons type on a principal fiber bundle with this group as its structure group. The connection to the usual Chern–Simons theory is established by utilizing a generalization, in the context of Cartan connections, of the notion of extension and reduction of connections. [ABSTRACT FROM AUTHOR]

In this paper, we propose two types of universal characters corresponding to partition shapes π = (3) and π = (2, 1) and construct their vertex operators realizations. It is proved that (3)-type and (2, 1)-type universal characters can be derived by the products of vertex operators acting on the identity. Furthermore, we investigate (3)-type and (2, 1)-type universal characters by means of Hamiltonian and fermions expectation values. In addition, based upon bilinear equations, we present the (3)-type and (2, 1)-type universal characters hierarchies whose τ functions can be derived from (3)-type and (2, 1)-type universal characters. [ABSTRACT FROM AUTHOR]

Let D V I be an exceptional domain of tube type and let Hν the associated generalized Hua operator. In this paper, we determine the explicit formula of the action of the group E7(−25) on D V I . We compute explicitly the value of the generalized Hua operator on D V I . Also, we characterized the Lp-range, 1 ≤ p < ∞ of the generalized Poisson transform on the Shilov boundary for the domain D V I . We prove that this range is a Hua–Hardy type spaces for functions satisfying a Hua system of differential equations. [ABSTRACT FROM AUTHOR]

In this article, we derive some new asymptotic properties of solution for a modified Camassa–Holm equation with cubic nonlinearity in weighted Sobolev spaces. Specifically, we prove that the strong solutions of Eq. (1.2) will maintain the corresponding decay properties provided the initial data ω0(x), ω0,x(x) decay logarithmically, algebraically and exponentially, respectively, which improves and extends the persistence properties of strong solutions to Eq. (1.2) obtained by Wu and Guo in paper [J. Math. Phys. 55, 081504 (2014)]. This method can be used to study the asymptotic decay properties for a class of Camassa–Holm equations. [ABSTRACT FROM AUTHOR]

In this paper, we construct, investigate and, in some cases, classify several new classes of (simple) modules over the Takiff s l 2 . More precisely, we first explicitly construct and classify, up to isomorphism, all modules over the Takiff s l 2 that are U h ̄ -free of rank one, where h ̄ is a natural Cartan subalgebra of the Takiff s l 2 . These split into three general families of modules. The sufficient and necessary conditions for simplicity of these modules are presented, and their isomorphism classes are determined. Using the vector space duality and Mathieu's twisting functors, these three classes of modules are used to construct new families of weight modules over the Takiff s l 2 . We give necessary and sufficient conditions for these weight modules to be simple and, in some cases, completely determine their submodule structure. [ABSTRACT FROM AUTHOR]