带有变磁扩散和磁耗散系数的三维不可压缩MHD方程组的整体强解

Global Strong Solution for Incompressible Mhd System with Variable Magnetic Diffusion and Magnetic Dissipation Coefficients

研究带有变磁扩散和磁耗散系数的三维不可压缩MHD方程组在边界光滑的有界区域Ω■R^3中的初边值问题,证明了当初值足够小并且满足自然的相容性条件时,MHD方程组存在唯一的局部强解,并且局部强解可以延拓为MHD方程组的整体强解.

In this paper,we study the initial boundary value problem of three dimensional incompressible MHD system with variable magnetic diffusion and magnetic dissipation coefficients in a bounded region Ω■R^3 with smooth boundary.The existence of the unique local strong solution to the MHD system is proved,and the local strong solution can be extended to the global strong solution of the MHD system.