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

Abstract

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 ‖ρ‖L∞(0,T;L∞)+‖ρ1/2u‖Ls(0,T;Lr)<∞ with 2/s+3/r≤1 and 3<r≤∞, then the strong solution will exist globally on R3×(0,T). In particular, the initial density may vanish on open sets, that is, the initial vacuum is allowed.