A new blowup criterion for strong solutions to the Cauchy problem of three-dimensional compressible magnetohydrodynamic equations

Abstract

In this paper, we establish a new blowup criterion for the strong solution to the Cauchy problem of the three-dimensional compressible MHD system with vacuum. Specifically, we obtain the blowup criterion in terms of Lt∞Lxq1-norm of the density and Lt∞Lx6-norm of the magnetic field. This criterion is closer to the basic energy and hence is superior to all the previous criterions in terms of the density and the magnetic field.