A BLOW-UP CRITERION FOR THREE-DIMENSIONAL COMPRESSIBLE MAGNETOHYDRODYNAMIC EQUATIONS WITH VARIABLE VISCOSITY

摘要

We are concerned with the breakdown of strong solutions to the three-dimensional compressible magnetohydrodynamic equations with density-dependent viscosity. It is shown that for the initial density away from vacuum, the strong solution exists globally if the gradient of the velocity satisfies parallel to del u parallel to(L2(0,T;L infinity)) infinity. Our method relies upon the delicate energy estimates and elliptic estimates.