相关论文: Global regularity for the 3D compressible magnetoh…
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 $…
In this paper, we investigate the incompressible viscous and resistive Hall magnetohydrodynamic equations (Hall MHD in short). We first study the regularity of the magneto-vorticity field $B+\omega$. In three dimensions, we derive some…
In this paper, we establish the global well-posedness of the incompressible magnetohydrodynamics (MHD) system on $n-$dimensional $(n\geq 2)$ periodic boxes with either no magnetic diffusivity (non-resistive case) or no fluid viscosity…
Finite-time blowup of solutions $(u(x,t),b(x,t))$ to a generalized system of equations with applications to ideal Magnetohydrodynamics (MHD) and one-dimensional fluid convection and stretching, among other areas, is investigated. The system…
In this paper, we establish an optimal blow-up criterion for classical solutions to the incompressible resistive Hall-magnetohydrodynamic equations. We also prove two global-in-time existence results of the classical solutions for small…
The three-dimensional (3D) full compressible magnetohydrodynamic system is studied in a general bounded domain with slip boundary condition for the velocity filed, adiabatic condition for the temperature and perfect conduction for the…
This paper concerns the Cauchy problem of the non-baratropic non-resistive magnetohydrodynamic (MHD) equations with zero heat conduction on the whole two-dimensional (2D) space with vacuum as far field density. By delicate weighted energy…
We construct and study global solutions for the 3-dimensional incompressible MHD systems with arbitrary small viscosity. In particular, we provide a rigorous justification for the following dynamical phenomenon observed in many contexts:…
This work is devoted to establish an improved blow-up criterion for strong solutions to a three-dimensional compressible non-Newtonian fluid with vacuum. The considered system is the Power Law model in a bounded periodic domain in R^3.We…
We study the global well-posedness of magnetohydrodynamic (MHD) equations. The hydrodynamic system consists of the Navier-Stokes equations for the fluid velocity coupled with a reduced from of the Maxwell equations for the magnetic field.…
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…
This paper focuses on the 2D compressible magnetohydrodynamic (MHD) equations without magnetic diffusion in a periodic domain. We present a systematic approach to establishing the global existence of smooth solutions when the initial data…
This paper is denoted to the study of dynamical behavior near explicit finite time blowup solutions for three dimensional incompressible Magnetohydrodynamics (MHD) equations. More precisely, we find a family of explicit finite time blowup…
This paper concerns the Cauchy problem of the two-dimensional (2D) nonhomogeneous incompressible Magnetohydrodynamic (MHD) equations with vacuum as far field density. We establish the global existence and uniqueness of strong solutions to…
For the equations of a planar magnetohydrodynamic (MHD) compressible flow with the viscosity depending on the specific volume of the gas and the heat conductivity being proportional to a positive power of the temperature, we obtain global…
The global existence of strong solutions to the compressible viscous magnetohydrodynamic (MHD) equations in $\mathbb{R}^3$ remains a significant open problem. When there is no magnetic diffusion, even small data global well-posedness is…
We study the local existence of solutions to the magnetohydrodynamics (MHD) system describing the motion of a compressible, viscous, electrically and heat conducting fluid in the $L^p-L^q$ class with inhomogeneous boundary conditions. The…
In this paper we show the global well-posedness of solutions to a three-dimensional magnetohydrodynamical (MHD) model in porous media. Compared to the classical MHD equations, our system involves a nonlinear damping term in the momentum…
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.
We are concerned with the study of the Cauchy problem to the 3D compressible Hall-magnetohydrodynamic system. We first establish the unique global solvability of strong solutions to the system when the initial data are close to a stable…