A Blow-up Criterion for Two Dimensional Compressible Viscous Heat-Conductive Flows

TL;DR

This paper establishes a criterion for the blow-up of solutions in 2D compressible viscous heat-conductive flows based on the upper bounds of density and temperature, allowing initial vacuum conditions.

Contribution

It introduces a new blow-up criterion involving density and temperature bounds for 2D compressible flows with initial vacuum.

Findings

Blow-up occurs if density or temperature bounds are exceeded.

The criterion applies even with initial vacuum conditions.

Provides conditions for global existence of solutions.

Abstract

We establish a blow-up criterion in terms of the upper bound of the density and temperature for the strong solution to 2D compressible viscous heat-conductive flows. The initial vacuum is allowed.