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

2020/11/24 by Li, Minling, Yao, Zheng-an, Yu, Rongfeng
#Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.2011.11968

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.

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