A new blowup criterion for strong solutions to the three-dimensional compressible magnetohydrodynamic equations with vacuum in a bounded domain

摘要

In this paper, we establish a new blowup criterions for the strong solution to the Dirichlet problem of the three-dimensional compressible MHD system with vacuum. Specifically, we obtain the blowup criterion in terms of the concentration of density in BMO norm or the concentration of the integrability of the magnetic field at the first singular time. The BMO-type estimate for the Lam e system and a variant of the Brezis-Waigner's inequality play a critical role in the proof. Copyright (c) 2017 John Wiley & Sons, Ltd.