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arXiv · 1808.07649

Global Well-Posedness and Large-Time Behavior of 1D Compressible Navier-Stokes System with Density-Depending Viscosity and Vacuum in Unbounded Domains

Kexin Li·Boqiang Lü·Yixuan Wang
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Abstract

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-dependent viscosity and large external force. Under a general assumption on the density-dependent viscosity, we prove that the Cauchy problem admits a unique global strong (classical) solution for the large initial data with vacuum. Moreover, the density is proved to be bounded from above time-independently. As a consequence, we obtain the large time behavior of the solution without external forces.

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Kexin Li, Boqiang Lü, Yixuan Wang. 2018-08-23. Global Well-Posedness and Large-Time Behavior of 1D Compressible Navier-Stokes System with Density-Depending Viscosity and Vacuum in Unbounded Domains. https://arxiv.org/abs/1808.07649

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