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Global strong solutions of the Cauchy problem for 1D compressible Navier-Stokes equations with density-dependent viscosity

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Abstract

We consider the Cauchy problem for one-dimensional compressible isentropic Navier-Stokes equations with density-dependent viscosity μ(ρ) = Aρα, where α > 0 and A > 0. The global existence of strong solutions is obtained, which improves the previous results by enlarging the interval of α. Moreover, our result shows that no vacuum is developed in a finite time provided the initial data does not contain vacuum.

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Acknowledgements

The authors would like to thank the referees for the valuable comments and suggestions which improve the presentation of the paper.

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Authors and Affiliations

  1. School of Mathematics, Liaoning University, Shenyang, 110036, China

    Sheng-quan Liu

  2. School of Mathematical Sciences, Xiamen University, Xiamen, 361005, China

    Sheng-quan Liu & Jun-ning Zhao

Authors
  1. Sheng-quan Liu
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  2. Jun-ning Zhao
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Correspondence to Sheng-quan Liu.

Additional information

The first author is supported by the National Natural Science Foundation of China under Grant No. 11301244, the Foundation of Education Department of Liaoning Province of China under Grant L2013006, and the Doctor Startup Foundation of Liaoning Province of China Grant 20131040. The second author is supported by the National Natural Science Foundation of China under Grant No. 11371297.

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Liu, Sq., Zhao, Jn. Global strong solutions of the Cauchy problem for 1D compressible Navier-Stokes equations with density-dependent viscosity. Acta Math. Appl. Sin. Engl. Ser. 33, 25–34 (2017). https://doi.org/10.1007/s10255-016-0631-4

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  • DOI: https://doi.org/10.1007/s10255-016-0631-4

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