A Blow-Up Criterion For 3D Compressible Naiver-Stokes Equations With Vacuum

In this paper,we establish a blow-up criterion in terms of the L∞ norm of the density ρand the pressure P for strong solutions 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；L∞(R3)) is upper bounded.The appearance of vaccum could be allowed.