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arXiv · 0901.0352

Compressible flows with a density-dependent viscosity coefficient

Ting Zhang·Daoyuan Fang
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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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Ting Zhang, Daoyuan Fang. 2009-02-13. Compressible flows with a density-dependent viscosity coefficient. https://arxiv.org/abs/0901.0352

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