Search

We show the lifespan of a strong solution to the incompressible 3D axially symmetric Euler system in R 3 can be arbitrarily large if the initial swirl is small enough. A precise lower bound of the lifespan, depending on the size of ‖ ∇ × (v 0 , θ e θ) ‖ L ∞ , is given. This extends the conclusion of Danchin (Proc Am Math Soc 141:1979–1993, 2012), in which the domain must be distant from the axis of symmetry. This may help us to have a better understanding of the nonlinear framework and the blowup mechanism inherent in the 3D axisymmetric Euler equations. [ABSTRACT FROM AUTHOR]

Nowadays, the application of artificial intelligence (AI) algorithms and techniques is ubiquitous and transversal. Fields that take advantage of AI advances include sound and music processing. The advances in interdisciplinary research potentially yield new insights that may further advance the AI methods in this field. This special issue aims to report recent progress and spur new research lines in AI-driven sound and music processing, especially within interdisciplinary research scenarios. [ABSTRACT FROM AUTHOR]

The original Leray's problem concerns the well-posedness of weak solutions to the steady incompressible Navier-Stokes equations in a distorted pipe, which approach the Poiseuille flow subject to the no-slip boundary condition at spatial infinity. In this paper, the same problem with the Navier-slip boundary condition instead of the no-slip boundary condition, is addressed. Due to the complexity of the boundary condition, some new ideas, presented as follows, are introduced to handle the extra difficulties caused by boundary terms. First, the Poiseuille flow in the semi-infinite straight pipe with the Navier-slip boundary condition will be introduced, which will serve as the asymptotic profile of the solution to the generalized Leray's problem at spatial infinity. Second, a solenoidal vector function defined in the whole pipe, satisfying the Navier-slip boundary condition, having the designated flux and equalling the Poiseuille flow at a large distance, will be carefully constructed. This plays an important role in reformulating our problem. Third, the energy estimates depend on a combined L2-estimate of the gradient and the stress tensor of the velocity. [ABSTRACT FROM AUTHOR]

The global well-posedness of the 3D inviscid MHD-Boussinesq system, with large axisymmetric initial data, in the Sobolev space H m is given. To overcome difficulties that arise in the time-uniform H 1 estimate, a reformulated system of good unknowns is discovered and an intermediate estimate is shown. Based on the reformulated system, a Beale-Kato-Majda-type criterion of the inviscid MHD-Boussinesq system is verified. Then higher-order estimates are concluded by the classical energy method and estimates of commutators. At last, we show the H m norm of the global-in-time solution temporally grows no faster than a four times exponential function (∀ m ∈ N) . [ABSTRACT FROM AUTHOR]

In this paper, we give a BKM-type blow-up criterion, which involves only a single component of the velocity, for the inviscid axially symmetric Boussinesq system. More precisely, we will show that if the vorticity of the swirl part of the velocity belongs to L 1 (0 , T ∗ , L ∞) , then the solution is regular up to time T ∗ . At present, our results can not be easily generalized to the classical L t 1 B M O regularity criterion, which will be considered in our further works. [ABSTRACT FROM AUTHOR]

A one-component regularity criterion for the non-resistive axially symmetric Hall-MHD system is given in this paper. More precisely, we show that strong solutions to a family of axially symmetric initial data, whose velocity and current density have trivial swirl components, could be smoothly extended beyond a possible blow-up time T ∗ if and only if the swirl component of the magnetic field h θ satisfies a Beale-Kato-Majda-type criterion. See (1.5) below. This criterion is not trivial even if the velocity field vanishes since the quantity h θ r satisfies a partial Burgers' equation in this situation. [ABSTRACT FROM AUTHOR]

In this paper, we prove a single-component BKM-type regularity criterion for the inviscid axially symmetric Hall-MHD system. More precisely, we show that if the current density is swirl-free, then the L t 1 L x ∞ boundedness of partial vorticity (corresponding to curl of the swirl part of the velocity) implies regularity of the solution. The novelty of our result is that we only impose a critical regularity criterion on one component of the velocity which is new even if we ignore the magnetic field and consider only the 3D axially symmetric Euler equations. Our results can not be easily extended to the classical L t 1 B M O norm regularity criterion at present, which will be pursued in our further works. [ABSTRACT FROM AUTHOR]

In this paper, we study the hedging effectiveness of crude oil futures on the basis of the lower partial moments (LPMs). An improved kernel density estimation method is proposed to estimate the optimal hedge ratio. We investigate crude oil price hedging by contributing to the literature in the following twofold: First, unlike the existing studies which focus on univariate kernel density method, we use bivariate kernel density to calculate the estimated LPMs, wherein the two bandwidths of the bivariate kernel density are not limited to the same, which is our main innovation point. According to the criterion of minimizing the mean integrated square error, we derive the conditions that the optimal bandwidths satisfy. In the process of derivation, we make a distribution assumption locally in order to simplify calculation, but this type of local distribution assumption is far better than global distribution assumption used in parameter method theoretically and empirically. Second, in order to meet the requirement of bivariate kernel density for independent random variables, we adopt ARCH models to obtain the independent noises with related to the returns of crude oil spot and futures. Genetic algorithm is used to tune the parameters that maximize quasi-likelihood. Empirical results reveal that, at first, the hedging strategy based on the improved kernel density estimation method is of highly efficiency, and then it achieves better performance than the hedging strategy based on the traditional parametric method. We also compare the risk control effectiveness of static hedge ratio vs. time-varying hedge ratio and find that static hedging has a better performance than time-varying hedging. [ABSTRACT FROM AUTHOR]

In this paper, we derive the Liouville theorem of D-solutions to the stationary MHD system under the asymptotic assumption: one of the velocity field and the magnetic field approaches zero and the other approaches a non zero constant vector at infinity. Our result extends the corresponding one of D-solutions to the Navier–Stokes equations when the velocity approaches a non zero constant vector at infinity. [ABSTRACT FROM AUTHOR]

South China is the most important uranium producer in the country. Much of the Mesozoic-Cenozoic geology of this area was dominated by NNE-trending intracontinental strike-slip faulting that resulted from oblique subduction of the paleo-Pacific plate underneath the eastern China continent. This strike-slip fault system was characterized by transpression in the early-mid Jurassic and by transtension from the latest Jurassic through Cretaceous to early Tertiary. Most uranium ore deposits in South China are strictly fault-hosted and associated with mid-late Mesozoic granitic intrusions and volcanic rocks, which formed under transpression and transtension regimes, respectively. Various data demonstrate that the NNE-trending strike-slip faults have played critical roles in the formation and distribution of hydrothermal uranium deposits. Extensive geochronological studies show that a majority of uranium deposits in South China formed during the time period of 140–40 Ma with peak ages between 87–48 Ma, coinciding well with the time interval of transtension. However, hydrothermal uranium deposits are not uniformly distributed along individual strike-slip fault. The most important ore-hosting segments are pull-apart stepovers, splay structures, extensional strike-slip duplexes, releasing bends and fault intersections. This non-uniform distribution of ore occurrences in individual fault zone reflects localization of hydrothermal fluids within those segments that were highly dilational and thus extremely permeable. The unique geometric patterns and structural styles of strike-slip faults may have facilitated mixing of deeply derived and near-surface fluids, as evidenced by stable isotopic data from many uranium deposits in South China. The identification of fault segments favorable for uranium mineralization in South China is important for understanding the genesis of hydrothermal ore deposits within continental strike-slip faults, and therefore has great implications for exploration strategies. [ABSTRACT FROM AUTHOR]

In this paper, we study the stationary magnetohydrodynamics system in R 2 × T . We prove trivialness of D-solutions (the velocity field u and the magnetic field h) when they are swirl-free. Meanwhile, this Liouville type theorem also holds provided u is swirl-free and h is axially symmetric, or both u and h are axially symmetric. Our method is also valid for certain related boundary value problems in the slab R 2 × [ - π , π ] . [ABSTRACT FROM AUTHOR]