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

摘要: 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 \!\text·\! n = \rmcurlH = 0，证明了初始密度含真空强解新的爆破准则：如果\left\| \rmdivu \right\|_L^1\left( 0,T;L^\infty \right) + \left\| H \right\|_L^\infty \left( 0,T;L^4 \right) < \infty ，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。

Abstract: 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 \!\text·\! n = \rmcurlH = 0. It is proved that the two-dimensional compressible heat conducting magnetohydrodynamic equations admit a global strong solution with large initial data provided that \left\| \rmdivu \right\|_L^1\left( 0,T;L^\infty \right) + \left\| H \right\|_L^\infty \left( 0,T;L^4 \right) < \infty .