A new blow-up criterion for the 2D full compressible Navier–Stokes equations without heat conduction in a bounded domain

Abstract

This paper is to derive a new blow-up criterion for the 2D full compressible Navier–Stokes equations without heat conduction in terms of the density ρ and the pressure P. More precisely, it indicates that in a bounded domain the strong solution exists globally if the norm ||ρ||L∞(0,t;L∞)+||P||Lp0(0,t;L∞)<∞ for some constant p0 satisfying 1<p0≤2. The boundary condition is imposed as a Navier-slip boundary one and the initial vacuum is permitted. Our result extends previous one which is stated as ||ρ||L∞(0,t;L∞)+||P||L∞(0,t;L∞)<∞.