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 (8)

• Vanishing of vacuum states and blow-up phenomena of the compressible Navier-Stokes equations
• Existence of Global Weak Solutions for 3D Degenerate Compressible Navier-Stokes Equations
• Global Well-Posedness and Large Time Asymptotic Behavior of Classical Solutions to the Compressible Navier-Stokes Equations with Vacuum
• Some Uniform Estimates and Large-Time Behavior for One-Dimensional Compressible Navier-Stokes System in Unbounded Domains with Large Data
• Blow up of smooth highly decreasing at infinity solutions to the compressible Navier-Stokes equations
• Global Existence of Weak Solutions to the Barotropic Compressible Navier-Stokes Flows with Degenerate Viscosities
• Non-Existence of Classical Solutions with Finite Energy to the Cauchy Problem of the Compressible Navier-Stokes Equations
• Global well-posedness of regular solutions to the three-dimensional isentropic compressible Navier-Stokes Equations with degenerate viscosities and vacuum