Global well-posedness and large-time behavior of 1D compressible Navier-Stokes equations with density-depending viscosity and vacuum in unbounded domains

• 作者: Kexin Li Boqiang Lü Yixuan Wang
• 来源期刊: 中国科学：数学（英文版）
• 年，卷（期）: 2021,（6）
• 所属期刊栏目: Articles
• 页码范围: 1231-1244
• 页数: 14页
• 语种: 英文

摘要

We consider the Cauchy problem for one-dimensional (1D) barotropic compressible Navier-Stokes equations with density-depending viscosity and large external forces.Under a general assumption on the density-depending 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.