Energy conservation for the weak solutions to the equations of compressible magnetohydrodynamic flows in three dimensions
Analysis of PDEs
2019-06-26 v1
Abstract
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.
Cite
@article{arxiv.1906.10371,
title = {Energy conservation for the weak solutions to the equations of compressible magnetohydrodynamic flows in three dimensions},
author = {Tingsheng Wang and Xinhua Zhao and Yingshan Chen and Mei Zhang},
journal= {arXiv preprint arXiv:1906.10371},
year = {2019}
}