Blow-up criterion for the 3D compressible non-isentropic Navier–Stokes equations without thermal conductivity

Abstract

In this paper, we prove a blow-up criterion in terms of the density ρ and the pressure P for the strong solutions with vacuum to Cauchy problem of the 3D compressible non-isentropic Navier–Stokes equations without thermal conductivity. More precisely, we show that the strong solution exists globally if the norm ‖(ρ,P)‖L∞([0,T]×R3) is bounded from above.