In this paper, we establish a blow up criterion for strong solutions of the full compressible Navier-Stokes equations just in terms of the gradient of the velocity. It shows that the gradient of the velocity alone dominates the global existence of strong solutions.
"A Blowup Criterion for the Full Compressible Navier-Stokes Equations." Methods Appl. Anal. 16 (4) 491 - 506, December 2009.