Blow-up of the smooth solutions to the compressible Navier-Stokes equations

摘要

In this paper, we will firstly extend the results about Jiu, Wang, and Xin (JDE, 2015, 259, 2981-3003). We prove that any smooth solution of compressible fluid will blow up without any restriction about the specific heat ratio gamma. Then we prove the blow-up of smooth solution of compressible Navier-Stokes equations in half space with Navier-slip boundary. The main ideal is constructing the differential inequality. Copyright (C) 2017 JohnWiley & Sons, Ltd.