Regularity and energy conservation for compressible isentropic magnetohydrodynamic equations

Abstract

In this paper, we mainly study the local energy equation of the weak solutions of the compressible isentropic MHD equation defined on T 3. We prove that the regularity of the solution is sufficient to guarantee the balance of the total energy in the B ,∞ 3 ((0, T) × T 3) space. We adopt a variant of the method of Feireisl et al.

Regularity and energy conservation for the compressible MHD equations

“…另外, 相比于 可压缩 Euler 方程, 可压缩 MHD 方程还需要考虑磁场 B 的正则性对系统能量守恒的影响, 即需要 处理非线性项 curlB × B 以及 curl(u × B). 在如下定理 1.1 中, 我们利用条件 divB = 0, 将洛伦兹 力项 curlB × B 改写成导数形式, 并将该导数通过分部积分转移到试验函数上, 从而去掉了文献[19]…”