Some Serrin type blow-up criteria for the three-dimensional viscous compressible flows with large external potential force

TL;DR

This paper establishes a Serrin type blow-up criterion for 3D viscous compressible flows with large external potential force, showing conditions under which solutions remain globally regular.

Contribution

It extends blow-up criteria to include large external potential forces and removes velocity conditions in isothermal, vacuum-free flows.

Findings

Global existence of strong solutions under Serrin's condition and bounded density.

Removal of velocity condition in isothermal flows without vacuum.

Applicable to large external potential forces in 3D compressible Navier-Stokes equations.

Abstract

We provide a Serrin type blow-up criterion for the 3-D viscous compressible flows with large external potential force. For the Cauchy problem of the 3-D compressible Navier-Stokes system with potential force term, it can be proved that the strong solution exists globally if the velocity satisfies the Serrin's condition and the sup-norm of the density is bounded. Furthermore, in the case of isothermal flows with no vacuum, the Serrin's condition on the velocity can be removed from the claimed criterion.