Related papers: Global well-posedness of magnetohydrodynamic equat…
In this paper, we consider numerical approximations for solving the nonlinear magneto-hydrodynamical system, that couples the Navier-Stokes equations and Maxwell equations together. A challenging issue to solve this model numerically is…
In this paper we study the initial-boundary value problem for the magnetohydrodynamic system in three dimensional exterior domain. We show an existence theorem of global in time strong solution for small initial data and we also show its…
Whether or not the solution to the $2\frac{1}{2}$-dimensional Hall-magnetohydrodynamics system starting from smooth initial data preserves its regularity for all time remains a challenging open problem. Although the research direction on…
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…
We study 1+1 dimensional relativistic non-resistive magnetohydrodynamics (MHD) with longitudinal boost invariance and shear stress tensor. Several analytical solutions that describe the fluid temperature evolution under the equation of…
We are concerned on the possibility of finite time singularity in a partially viscous magnetohydrodynamic equations in $\Bbb R^n$, $n=2,3$, namely the MHD with positive viscosity and zero resistivity. In the special case of zero magnetic…
In this paper, we prove the energy conservation for the weak solutions to the three-dimensional equations of compressible magnetohydrodynamic flows (MHD) under certain conditions only about density and velocity. This work is inspired by the…
The evolution of two isothermal, incompressible, immiscible fluids in a bounded domain is governed by Cahn-Hilliard-Navier-Stokes equations (CHNS System). In this work, we study the well-posedness results for the CHNS system with…
In this article, the Cauchy problem of three-dimensional (3-D) incompressible magnetohydrodynamic system was investigated. If the initial $\mathcal{M}^{1,1}$ norms of the vorticity $\omega$ and the current density $j$ are both sufficiently…
This paper is concerned with existence of solutions to the incompressible non-resistive viscous magnetohydrodynamic (MHD) equations with large initial perturbations in there-dimensional (3D) periodic domains (in Lagrangian coordinates).…
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…
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…
The full compressible magnetohydrodynamic equations can be derived formally from the complete electromagnetic fluid system in some sense as the dielectric constant tends to zero. This process is usually referred as magnetohydrodynamic…
We show, using the spectral Galerkin method together with compactness arguments, existence and uniqueness of the periodic strong solutions for the magnetohydrodynamics's type equations with inhomogeneous boundary conditions. Also, we study…
We prove the global well-posedness of the Cauchy problem to the 3D incompressible Hall-magnetohydrodynamic system supplemented with initial data in critical Besov spaces, which generalize the result in [10]. Meanwhile , we analyze the…
We investigate the compressible magnetohydrodynamic equations subject to large external potential forces with discontinuous initial data in a three-dimensional bounded domain under Navier-slip boundary conditions. We show the global…
A fluid-particle system of the inhomogeneous Navier-Stokes equations and Vlasov equation in the three dimensional space is considered in this paper. The coupling arises from the drag force in the fluid equations and the acceleration in the…
We consider a Large Eddy Simulation model for a homogeneous incompressible Newtonian fluid in a box space domain with periodic boundary conditions on the lateral boundaries and homogeneous Dirichlet conditions on the top and bottom…
In this paper, we study a hydrodynamic system modeling the deformation of vesicle membranes in incompressible viscous fluids. The system consists of the Navier-Stokes equations coupled with a fourth order phase-field equation. In the three…
In this brief note we study the $n$-dimensional magnetohydrodynamic equations with hyper-viscosity and zero resistivity. We prove global regularity of solutions when the hyper-viscosity is sufficiently strong.