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This paper concentrates on the global existence of weak solutions in L p with finite energy to a type of one-dimensional compressible Euler-Vlasov equations, which models the interaction between the isentropic gas and dispersed particles. Approximate solutions are constructed by adding artificial viscosity. Then the uniform L p estimates of the approximate solutions with respect to the artificial viscosity are established through some subtle analysis on level sets of density and relative velocity. The convergence of approximate solutions to the desired weak solutions is guaranteed by the L p compensated compactness framework. [ABSTRACT FROM AUTHOR]

In this paper, the three-dimensional (3D) isentropic compressible Navier–Stokes equations with degenerate viscosities (ICND) is considered in both the whole space and the periodic domain. First, for the corresponding Cauchy problem, when shear and bulk viscosity coefficients are both given as a constant multiple of the density's power ( ρ δ with 0 < δ < 1 ), based on some elaborate analysis of this system's intrinsic singular structures, we show that the L ∞ norm of the deformation tensor D(u) and the L 6 norm of ∇ ρ δ - 1 control the possible breakdown of regular solutions with far field vacuum. This conclusion means that if a solution with far field vacuum of the ICND system is initially regular and loses its regularity at some later time, then the formation of singularity must be caused by losing the bound of D(u) or ∇ ρ δ - 1 as the critical time approaches. Second, when 0 < δ ≤ 1 , under the additional assumption that the shear and second viscosities (respectively μ (ρ) and λ (ρ) ) satisfy the BD relation λ (ρ) = 2 (μ ′ (ρ) ρ - μ (ρ)) , if we consider the corresponding problem in some periodic domain and the initial density is away from the vacuum, it can be proved that the possible breakdown of classical solutions can be controlled only by the L ∞ norm of D(u). It is worth pointing out that, except the conclusions mentioned above, another purpose of the current paper is to show how to understand the intrinsic singular structures of the fluid system considered now, and then how to develop the corresponding nonlinear energy estimates in the specially designed energy space with singular weights for the unique regular solution with finite energy. [ABSTRACT FROM AUTHOR]

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This article considers the existence of global smooth solutions to the Cauchy problem in 3D incompressible magnetohydrodynamic (MHD) flows, and prove the global regularity of classical solutions for a family of large initial data with finite energy. [ABSTRACT FROM AUTHOR]

The goal of this paper is to determine analytical expression for the spectral density function of a signal, affected by a known frequency transformation, which do not modify the process energy. Such transformations of frequency variable can frequently appear on spectral density function of a signal, due to physical events (e.g. Doppler effect) or mathematical considerations (e.g. changing the coordinate system). In this case, all components of the spectral density function are modified. The formulas are valid for every spectral component and can be used in signal processing, for model simulation or implementation of advanced algorithm. A case study is illustrated on wave spectrum correction.

We discuss a class of exact finite energy solutions to the vacuum source-free Maxwell field equations as models for multi- and single cycle laser pulses in classical interaction with relativistic charged test particles. These solutions are classified in terms of their chiral content based on their influence on particular charge configurations in space. Such solutions offer a computationally efficient parameterization of compact laser pulses used in laser-matter simulations and provide a potential means for experimentally bounding the fundamental length scale in the generalized electrodynamics of Bopp, Landé and Podolsky. [ABSTRACT FROM AUTHOR]

In this paper we prove the global existence of large amplitude finite energy solutions for a system describing Quantum Fluids with nonlinear nonlocal interaction terms. The system may also (but not necessarily) include dissipation terms which do not provide any help to get the global existence. The method is based on the polar factorization of the wave function (which somehow generalizes the WKB method), the construction of approximate solutions via a fractional step argument and the deduction of Strichartz type estimates for the approximate solutions. Finally local smoothing and a compactness argument of Lions Aubin type allow to show the convergence. [ABSTRACT FROM AUTHOR]

In this paper we construct a family of finite energy smooth solutions to the three-dimensional incompressible nematic liquid crystal flows. We achieve this by choosing the steady state Beltrami flows which have infinite energies as the initial data and using a special cut-off technique. [ABSTRACT FROM AUTHOR]

We construct a family of finite energy classical solutions to the 3D MHD system with both Laplacian dissipation and magnetic diffusion. We choose the steady state Beltrami flows as the initial data and use a cut-off technique to obtain the global regularity for all time t . [ABSTRACT FROM AUTHOR]