Blow-up criterion for 3-D compressible magnetohydrodynamics with vacuum and zero resistivity

We study strong solutions of the equations of compressible magnetohydrodynamics with zero resistivity in a domain Omega subset of R-3. We establish a criterion for possible breakdown of such solutions at a finite time in terms of both parallel to del u parallel to(L1(0,T;L infinity)). and parallel to theta parallel to(L infinity(0,T;L infinity)). More precisely, if a solution of 3D compressible magnetohydrodynamics with zero resistivity is initially regular and loses its regularity at some later time, then the loss of regularity implies growth without bound of both parallel to del u parallel to(L1(0,T;L infinity)). and parallel to theta parallel to(L infinity(0,T;L infinity)) as the critical time approaches. In addition, initial vacuum states are allowed in our cases. (C) 2012 Elsevier Inc. All rights reserved.