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Refined blow-up criteria for the three-dimensional viscous compressible flows with large external potential force and general pressure. (English) Zbl 1479.35635

Summary: 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.

MSC:

35Q30 Navier-Stokes equations
76N06 Compressible Navier-Stokes equations
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
35D35 Strong solutions to PDEs
35A01 Existence problems for PDEs: global existence, local existence, non-existence
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