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

TL;DR

This paper establishes an improved criterion for predicting the blow-up of strong solutions in a 3D compressible non-Newtonian fluid with vacuum, based on the velocity gradient norm, applicable for all power-law indices greater than 1.

Contribution

It introduces a new blow-up criterion for strong solutions of the 3D compressible non-Newtonian fluid system with vacuum, valid for any power-law index q > 1.

Findings

Blow-up criterion based on the L^4(0,T;L^{ }( )) norm of the velocity gradient.

Applicable to the Power Law model in bounded periodic domains.

Valid for all power-law indices q > 1.

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}({\Omega}))norm of the gradient of the velocity for any power-law index q is greater than 1.