二维可压缩热传导磁流体方程的爆破准则

On the Blow-up Criterion for Two-Dimensional Compressible Heat Conducting Magnetohydrodynamic Equations

研究了二维可压缩热传导磁流体方程的初边值问题,其中磁场H满足滑动边值条件H·n=curlH=0,证明了初始密度含真空强解新的爆破准则:如果║divu║L1(0,T;L∞)+║H║L∞(0,T;L4)<∞,则二维可压缩热传导磁流体方程初边值问题的大初值强解整体存在。

This paper proves a new blow-up criterion for the strong solution to the initial boundary value problem of two-dimensional compressible heat conducting magnetohydrodynamic equations with initial vacuum.Here,the magnetic field H satisfies the perfect conducting boundary condition H·n=curlH=0.It is proved that the two-dimensional compressible heat conducting magnetohydrodynamic equations admit a global strong solution with large initial data provided that║divu║L^1(0,T;L~∞)+║H║L~∞(0,T;L^4)<∞.