相关论文: The 2D Incompressible Magnetohydrodynamics Equatio…
In this paper, we prove global existence of solutions with analytic regularity to the 2D MHD boundary layer equations in the mixed Prandtl and Hartmann regime derived by formal multi-scale expansion in \cite{GP}. The analysis shows that the…
The Velocity-Vorticity (VV) formulation of the incompressible Navier-Stokes equations has become popular in recent years, especially in numerical studies, due to its structural advantages. Recently, with L. Rebholz, we introduced a Voigt…
In this paper, we consider two Approximate Deconvolution Magnetohydrodynamics models which are related to Large Eddy Simulation. We first study existence and uniqueness of solutions in the double viscous case. Then, we study existence and…
We prove higher-order and a Gevrey class (spatial analytic) regularity of solutions to the Euler-Voigt inviscid $\alpha$-regularization of the three-dimensional Euler equations of ideal incompressible fluids. Moreover, we establish the…
We use De Giorgi techniques to prove H\"older continuity of weak solutions to a class of drift-diffusion equations, with $L^2$ initial data and divergence free drift velocity that lies in $L_{t}^{\infty}BMO_{x}^{-1}$. We apply this result…
We obtain the global well-posedness to the 3D incompressible magnetohydrodynamics (MHD) equations in Besov space with negative index of regularity. Particularly, we can get the global solutions for a new class of large initial data. As a…
This paper establishes the global existence and uniqueness of smooth solutions to the two-dimensional compressible magnetohydrodynamic system when the initial data is close to an equilibrium state. In addition, explicit large-time decay…
In this paper we show that the solutions to the incompressible Hall-MHD system with fractional magnetic diffusion depend continuously on the initial data in $H^s(\mathbb{R}^d)$, $s>1+\frac{d}{2}$.
In this paper, we prove the global well-posedness for the three-dimensional magnetohydrodynamics (MHD) equations with zero viscosity and axisymmetric initial data. First, we analyze the problem corresponding to the Sobolev regularities $…
This paper is concerned with the stability and large-time behavior of 3D incompressible MHD equations with only vertical dissipation near a background magnetic field. By making full use of the dissipation generated by the background…
This paper is dedicated to the Oldroyd-B model with fractional dissipation $(-\Delta)^{\alpha}\tau$ for any $\alpha>0$. We establish the global smooth solutions to the Oldroyd-B model in the corotational case with arbitrarily small…
We describe a numerical code to solve the equations for ideal magnetohydrodynamics (MHD). It is based on an explicit finite difference scheme on an Eulerian grid, called the Total Variation Diminishing (TVD) scheme, which is a…
We study the $2\frac12$-dimensional electron magnetohydrodynamics (EMHD) system on $\mathbb T^2$ with componentwise fractional dissipation: $\partial_t a+a_yb_x-a_xb_y=-\Lambda^\alpha a$ and $\partial_t b-a_y\Delta a_x+a_x\Delta…
This article examines the existence and uniqueness of weak solutions to the d-dimensional micropolar equations ($d=2$ or $d=3$) with general fractional dissipation $(-\Delta)^{\alpha}u$ and $(-\Delta)^{\beta}w$. The micropolar equations…
The paper presents two contributions in the context of the numerical simulation of magnetized fluid dynamics. First, we show how to extend the ideal magnetohydrodynamics (MHD) equations with an inbuilt magnetic field divergence cleaning…
Besides total energy, three-dimensional incompressible Hall magnetohydrodynamics (MHD) possesses two inviscid invariants which are the magnetic helicity and the generalized helicity. New exact relations are derived for homogeneous…
The magnetohydrodynamic current-vortex sheet is a free boundary problem involving a moving free surface separating two plasma regions. We prove the global nonlinear stability of current-vortex sheet in the two dimensional ideal…
A multi-symplectic formulation of ideal magnetohydrodynamics (MHD) is developed based on a Clebsch variable variational principle in which the Lagrangian consists of the kinetic minus the potential energy of the MHD fluid modified by…
In this paper we present an analytical study of a subgrid scale turbulence model of the three-dimensional magnetohydrodynamic (MHD) equations, inspired by the Navier-Stokes-alpha (also known as the viscous Camassa-Holm equations or the…
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…