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 $B_3^{\alpha ,\infty }((0,T)\times {𝕋}^3)$ space. We adopt a variant of the method of Feireisl et al.

中文翻译：

---

可压缩等熵磁流体力学方程的正则和守恒

在本文中，我们主要研究可压缩的等熵MHD方程的弱解的局部能量方程。 ${𝕋}^3$。我们证明了解决方案的规律性足以保证平衡中总能量的平衡。${乙}_3^{\alpha ，\infty }（（0，Ť）\times {𝕋}^3）$空间。我们采用Feireisl等人方法的一种变体。