Energy conservation for the weak solutions to the equations of compressible magnetohydrodynamic flows in three dimensions

Tingsheng Wang, Xinhua Zhao, Yingshan Chen, Mei Zhang

Published 2019-06-25Version 1

In this paper, we prove the energy conservation for the weak solutions to the three-dimensional equations of compressible magnetohydrodynamic flows (MHD) under certain conditions only about density and velocity. This work is inspired by the seminal work by Yu [27] on the energy conservation of compressible Navier-Stokes equations. Our result indicates that even the magnetic field is taken into account, we only need some regularity conditions of the density and velocity as in [27] to ensure the energy conservation.