Energy conservation for compressible magnetohydrodynamics equations

In this paper, we study the problem of energy conservation for compressible magnetohydrodynamic(MHD) system in ( 0 , T ) × T 3 . We obtain sufficient regularity conditions of weak solutions for the MHD system to satisfy the energy conservation. This work is inspired by Feireisl et al. [1] and Wiedemann et al. [2], which study the energy conservation problem of compressible isentropic Euler equations and Navier-Stokes equations. Compared with [1,2], we consider the MHD equations with a general viscosity coefficient, which makes the analysis more complicated.