Blowup criterion for the three-dimensional equations of compressible viscous micropolar fluids with vacuum

In this paper, we prove a blowup criterion of strong solutions to the Cauchy problem for the three-dimensional equations of compressible viscous micropolar fluids. It is shown that if the density and the velocity satisfy parallel to rho parallel to(L infinity (0,T;L infinity)) + parallel to rho(1/2)u parallel to(Ls(0,T;Lr)) < infinity with 2/s + 3/r <= 1 and 3 < r <= infinity, then the strong solution will exist globally on R-3 x (0, T). In particular, the initial density may vanish on open sets, that is, the initial vacuum is allowed. (C) 2012 Elsevier Ltd. All rights reserved.