Regularity and energy conservation for the compressible MHD equations

Abstract

In this paper, we aRemark concerned with the regularity and energy conservation of the weak solutions for inhomogeneous compressible ideal MHD (magnetohydrodynamics) systems. We give two sufficient 条件 on the regularity of solutions in order to ensuRemark the energy to be conserved, wheRemark $(t,~x)\in~(0,~T)\times\mathbb{T}^d$ $(d\geq~1)$. The main tool we have employed relies on the commutator estimates similar to those used by Constantin et al. (1994) for the homogeneous incompressible Euler equations.