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

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Abstract

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.

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Acknowledgements

This work was supported by Undergraduate Research Fund of Beijing Normal University (Grant Nos. 2017-150 and 201810027047), and National Natural Science Foundation of China (Grant Nos. 11601218 and 11771382).

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Authors and Affiliations

  1. School of Mathematical Sciences, Beijing Normal University, Beijing, 100875, China

    Kexin Li

  2. College of Mathematics and Information Science, Nanchang Hangkong University, Nanchang, 330063, China

    Boqiang Lü

  3. Institute of Applied Mathematics, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, China

    Yixuan Wang

Authors
  1. Kexin Li
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  2. Boqiang Lü
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  3. Yixuan Wang
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Correspondence to Boqiang Lü.

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Li, K., Lü, B. & Wang, Y. Global well-posedness and large-time behavior of 1D compressible Navier-Stokes equations with density-depending viscosity and vacuum in unbounded domains. Sci. China Math. 64, 1231–1244 (2021). https://doi.org/10.1007/s11425-019-9521-4

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  • DOI: https://doi.org/10.1007/s11425-019-9521-4

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