相关论文: Existence and Stability of almost finite energy we…

In this paper we analyze a fully discrete scheme for a general Cahn-Hilliard equation coupled with a nonsteady Magneto-hydrodynamics flow, which describes two immiscible, incompressible and electrically conducting fluids with different…

We study a general convergence theory for the analysis of numerical solutions to the magnetohydrodynamic system describing the time evolution of compressible, viscous, electrically conducting fluids in space dimension d (= 2; 3). First, we…

We prove the non-uniqueness of weak solutions to 3D magnetohydrodynamic (MHD for short) equations. The constructed weak solutions do not conserve the magnetic helicity and can be close to any given smooth, divergence-free and mean-free…

We review recent progress in understanding nearly integrable models within the framework of generalized hydrodynamics (GHD). Integrable systems have infinitely many conserved quantities and stable quasiparticle excitations: when…

We study the Rayleigh-Taylor problem for two incompressible, immiscible, viscous magnetohydrodynamic (MHD) flows, with zero resistivity, surface tension (or without surface tenstion) and special initial magnetic field, evolving with a free…

In this paper, we study the existence of weak solutions to a steady system that describes the motion of a micropolar electrorheological fluid. The constitutive relations for the stress tensors belong to the class of generalized Newtonian…

Using a modified WKB approach, we present a rigorous semi-classical analysis for solutions of nonlinear Schroedinger equations with rotational forcing. This yields a rigorous justification for the hydrodynamical system of rotating…

(Abridged) We consider dynamics and turbulent interaction of whistler modes within the framework of inertialess electron MHD (EMHD). We argue there is no energy principle in EMHD: any stationary closed configuration is neutrally stable. We…

In this paper, we consider exterior problem of the critical semilinear wave equation in three space dimensions with variable coefficients and prove global existence of smooth solutions. Similar to the constant coefficients case, we show…

In this paper we consider the 2D Ericksen-Leslie equations which describes the hydrodynamics of nematic Liquid crystal with external body forces and anisotropic energy modeling the energy of applied external control such as magnetic or…

The present paper considers the full nonlinear dynamics of a homogeneous bubble inside an unbounded isentropic compressible inviscid liquid. This model is described by a free-boundary problem of compressible Euler equations with nonlinear…

We propose a result of global stability for the equations of homogeneous, incompressible magnetohydrodynamics (MHD) on a torus of any dimension $d \in \{2,3,...\}$, with positive viscosity and resistivity. This result applies to the…

In this article, we prove various illposedness results for the Cauchy problem for the incompressible Hall- and electron-magnetohydrodynamic (MHD) equations without resistivity. These PDEs are fluid descriptions of plasmas, where the effect…

The quantum dynamics of electron-nuclear systems is analyzed from the perspective of the exact factorization of the wavefunction, with the aim of defining gauge invariant equations of motion for both the nuclei and the electrons. For pure…

We show that the Fractional Quantum Hall Effect can be phenomenologically described as a special flow of a quantum incompressible Euler liquid. This flow consists of a large number of vortices of the same chirality. In this approach each…

The ideal magnetohydrodynamic equations are, roughly speaking, a quasi-linear symmetric hyperbolic system of PDEs, but not all the unknowns play the same role in this system. Indeed, in the regime of small magnetic fields, the equations are…

For an Euler system, with dynamics generated by a potential energy functional, we propose a functional format for the relative energy and derive a relative energy identity. The latter, when applied to specific energies, yields relative…

We establish both global existence and decay properties for solutions with small data for a general class of coupled system of tensorial quasilinear hyperbolic wave equations in three space dimensions, that covers the dynamical Einstein…

The hydrodynamic description of probabilistic ballistic annihilation, for which no conservation laws hold, is an intricate problem with hard sphere-like dynamics for which no exact solution exists. We consequently focus on simplified…

I consider the problem of weakly nonlinear stability of three-dimensional convective magnetohydrodynamic systems, where there is no alpha-effect or it is insignificant, to perturbations involving large scales. I assume that the convective…