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Free Boundary Value Problem for the Cylindrically Symmetric Compressible Navier-Stokes Equations with a Constant Exterior Pressure

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Abstract

This paper is concerned with the free boundary value problem (FBVP) for the cylindrically symmetric barotropic compressible Navier-Stokes equations (CNS) with density-dependent viscosity coefficients in the case that across the free surface stress tensor is balanced by a constant exterior pressure. Under certain assumptions imposed on the initial data, the unique cylindrically symmetric strong solution is shown to exist globally in time and tend to a non-vacuum equilibrium state exponentially as time tends to infinity.

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Acknowledgements

All authors contributed to each part of this work equally. The authors declare that they have no competing interests.

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Authors and Affiliations

  1. Institute of Atmospheric Physics, Chinese Academy of Sciences, Beijing, 100029, China

    Ru-xu Lian

  2. Guanghua School of Management, Peking University, Beijing, 100871, China

    Jun-li Wang

Authors
  1. Ru-xu Lian
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  2. Jun-li Wang
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Correspondence to Ru-xu Lian.

Additional information

The research is supported by National Natural Science Foundation of China (No. 41630530), Key Research Program of Frontier Sciences, CAS (Grant No. QYZDY-SSW-DQC002), National Natural Science Foundation of China (No. 41575109).

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Lian, Rx., Wang, Jl. Free Boundary Value Problem for the Cylindrically Symmetric Compressible Navier-Stokes Equations with a Constant Exterior Pressure. Acta Math. Appl. Sin. Engl. Ser. 34, 761–774 (2018). https://doi.org/10.1007/s10255-018-0785-3

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  • DOI: https://doi.org/10.1007/s10255-018-0785-3

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