Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure

We obtain some refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure. For the Cauchy problem of the 3-D compressible Navier–Stokes system with potential force term and general pressure, the strong solution exists globally if the velocity satisfies the Serrin’s condition and the sup-norm of the density is bounded. On the other hand, for the case without initial vacuum state, the blow-up criterion can be shown to be depending on density only. The proof is based on some new a priori estimates for 3-D compressible Navier–Stokes equations coupled with steady state solutions.