Non-existence of global classical solutions to barotropic compressible Navier-Stokes equations with degenerate viscosity and vacuum

Abstract

We are concerned about the barotropic compressible Navier-Stokes equations with density-dependent viscosities which may degenerate in vacuum. We show that any classical solution to barotropic compressible Navier-Stokes equations in bounded domains will blow up, when the initial density admits an isolated mass group and the viscousity coefficients satisfy some conditions. A new condition on viscosities is first put forward in this paper.

References in corpus (2)

• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• Blow up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations