Analysis on the Regularity of Solutions of Energy Conservation to the Compressible MHD Equations

ABSTRACT In our article, we give some sufficient conditions on the regularity of solutions to the compressible magnetohydrodynamics (MHD) equations on (d 2) for the point‐wise energy conservation, which is different from the energy conservation in the sense of distribution obtained by Wu and Tan (2019). Our strategy relies on commutator estimates similar to those employed by Chen and Yu (2019) for the non‐homogeneous incompressible Euler equations. Furthermore, we have adopted the methodology of Wang, Ye and Yu (2023); Wu and Zhou (2023) into our approach.