| Magnetohydrodynamics (MHD)(magneto fluid dynamics or hydromagnetics) is an academic discipline which studies the dynamics of electrically conducting fluids. The MHD is mainly used to study the problem of the influence of the ideal conductive fluid on the movement of magnetic field and the influence of the fluid resistance on the magnetic fields as the fluid is static, including magnetic freeze and magnetic diffusion. Its stickiness disappeared limit problem is mainly used in three aspects: astrophysics, controlled thermonuclear reactions and industrial.The theoretical research has classic and fundamental significance in fluid dynamics and the perturbation theory.This paper mainly studies the solvability,regularity and vanishing viscosity limit of the3D viscous magnetohydrodynamic system in a class of bounded domains with a slip boundary condition.The research content is as follows:The first chapter is the introduction part, mainly introduced the academic background and its theoretical and practical significance; Literature review both at home and abroad and the related research progress and achievements and the deficiencies and problems that need further research and the origin of this research topic and main research content.The second chapter mainly gives some basic knowledge and notations, which will be used later.The third chapter is using Galerkin approximation method to establish the global existence of the weak solution of MHD equations, as well as the next section to consider generally smooth and bounded connected region in the three-dimensional space. And investigates the well-posedness and its regularity of higher order of the strong solution of the viscous MHD equations.Chapter iv consider the evolutionary MHD systems, and study the the regularity and vanishing viscosity limit of the3-D viscous system in a class of bounded domains with a slip boundary condition. We derive the convergence in a sence if the initial date holds some sufficient conditions. |
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