Compressible flows with a density-dependent viscosity coefficient

2009/01/04 by Zhang, Ting, Fang, Daoyuan
#35Q35 #Analysis of PDEs (math.AP) #FOS: Mathematics

paper · doi:10.48550/arxiv.0901.0352

Abstract

We prove the global existence of weak solutions for the 2-D compressible Navier-Stokes equations with a density-dependent viscosity coefficient (λ=λ(ρ)). Initial data and solutions are small in energy-norm with nonnegative densities having arbitrarily large sup-norm. Then, we show that if there is a vacuum domain at the initial time, then the vacuum domain will retain for all time, and vanishes as time goes to infinity. At last, we show that the condition of μ=constant will induce a singularity of the system at vacuum. Thus, the viscosity coefficient μ plays a key role in the Navier-Stokes equations.

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