Blow-up criterion for a three-dimensional compressible non-Newtonian fluid with vacuum

Abstract

This work is devoted to establish an improved blow-up criterion for strong solutions to a three-dimensional compressible non-Newtonian fluid with vacuum. The considered system is the Power Law model in a bounded periodic domain in R^3.We establish a blow-up criterion for the local strong solutions in terms of the L^4(0,T;L^{\infty}(Ω))norm of the gradient of the velocity for any power-law index q is greater than 1.

15 pages,0 figures