Preprint 2009-031
A blow-up criterion for compressible viscous heat-conductive flows
Jishan Fan, Song Jiang and Yaobin Ou
Abstract: We study an initial boundary value problem for the three-dimensional Navier–Stokes equations of viscous heat-conductive fluids in a bounded smooth domain. We establish a blow-up criterion for the local strong solutions in terms of the temperature and the gradient of the velocity only, similar to the Beale–Kato–Majda criterion for ideal incompressible flows.