相关论文: Existence and Stability of almost finite energy we…
We study the Cauchy problem of three-dimensional compressible non-isentropic magnetohydrodynamic (MHD) fluids with both interior and far field vacuum states. Applying delicate energy estimates, initial layer analysis, and continuation…
We consider the ideal magnetohydrodynamics (MHD) of a shallow fluid layer on a rapidly rotating planet or star. The presence of a background toroidal magnetic field is assumed, and the "shallow water" beta-plane approximation is used. We…
We introduce a novel structure-preserving method in order to approximate the compressible ideal Magnetohydrodynamics (MHD) equations. This technique addresses the MHD equations using a non-divergence formulation, where the contributions of…
We prove the existence of both local and global smooth solutions to the Cauchy problem in $\R^3$ for the incompressible magnetohydrodynamics (MHD) system. We also prove that the solution to the incompressible MHD system can be obtained as…
We establish the existence of axially symmetric weak solutions to steady incompressible magnetohydrodynamics with non-homogeneous boundary conditions. The key issue is the Bernoulli's law for the total head pressure $\Phi=\f 12(|{\bf…
In this paper, we consider the quantum MHD equations with both the viscosity coefficient and the magnetic diffusion coefficient are depend on the density. we prove the global existence of weak solutions and perform the lower planck limit in…
We investigate the non-uniqueness of weak solutions of the Quantum-Hydrodynamic system. This form of ill-posedness is related to the change of the number of connected components of the support of the position density (called nodal domains)…
In this paper, we provide a much simplified proof of the main result in [Lin, Xu, Zhang, arXiv:1302.5877] concerning the global existence and uniqueness of smooth solutions to the Cauchy problem for a 2D incompressible viscous and…
In this paper we deal with weak solutions to the Maxwell-Landau-Lifshitz equations and to the Hall-Magneto-Hydrodynamic equations. First we prove that these solutions satisfy some weak-strong uniqueness property. Then we investigate the…
This paper extends the author's previous analysis in \cite{AMZ3} on weak solutions with large norms for the collisional quantum hydrodynamic (QHD) equations in semiconductor modeling to 2-dimensional tori. We first establish the global…
The generalized hydrodynamic (GHD) approach has been extremely successful in describing the out-of-equilibrium properties of a great variety of integrable many-body quantum systems. It naturally extracts the large-scale dynamical degrees of…
I consider the problem of weakly nonlinear stability of three-dimensional parity-invariant magnetohydrodynamic systems to perturbations, involving large scales. I assume that the MHD state, the stability of which I investigate, does not…
This paper is concerned with a compressible MHD equations describing the evolution of viscous non-resistive fluids in piecewise regular bounded Lipschitz domains. Under the general inflow-outflow boundary conditions, we prove existence of…
We are concerned with the global existence of finite energy weak solutions to 3D density-dependent magnetohydrodynamics (MHD) system with Hall-effect set in a general smooth bounded domain. The perfectly conducting wall boundary condition…
We show that an infinite number of non-unitary minimal models may describe two dimensional turbulent magnetohydrodynamics (MHD), both in the presence and absence of the Alf'ven effect. We argue that the existence of a critical dynamical…
This paper studies the global well-posedness of the incompressible magnetohydrodynamic (MHD) system with a velocity damping term. We establish the global existence and uniqueness of smooth solutions when the initial data is close to an…
In this paper, we prove the non-uniqueness of three-dimensional magneto-hydrodynamic (MHD) system in $C([0,T];L^2(\mathbb{T}^3))$ for any initial data in $H^{\bar{\beta}}(\mathbb{T}^3)$~($\bar{\beta}>0$), by exhibiting that the total energy…
The quantum hydrodynamic model for charged particle systems is extended to the cases of non zero magnetic fields. In this way, quantum corrections to magnetohydrodynamics are obtained starting from the quantum hydrodynamical model with…
The quasi-geostrophic two-layer (QS2L) system models the dynamic evolution of two interconnected potential vorticities, each is governed by an active scalar equation. These vorticities are linked through a distinctive combination of their…
We consider a two-dimensional MHD model describing the evolution of viscous, compressible and electrically conducting fluids under the action of vertical magnetic field without resistivity. Existence of global weak solutions is established…