A blow-up criterion for strong solutions to three-dimensional compressible magnetohydrodynamic equations

Abstract

We are concerned with an initial boundary value problem for the compressible magnetohydrodynamic equations with viscosity depending on the density. It is show that for the initial density away from vacuum, the strong solution to the problem exists globally if the gradient of velocity satisfies $\Vert \nabla \mathbf{u}{\Vert }_{L^2(0,T;L^{\infty })}<\infty$. Our method relies upon the delicate energy estimates and elliptic estimates.

17 pages

References in corpus (3)

• Global solutions to the three-dimensional full compressible magnetohydrodynamic flows
• On Local Strong Solutions to the Cauchy Problem of Two-Dimensional Density-Dependent Magnetohydrodynamic Equations with Vacuum
• A regularity criterion for the weak solutions to the Navier-Stokes-Fourier system