Articles

GLOBAL STABILITY OF WAVE PATTERNS FOR COMPRESSIBLE NAVIER-STOKES SYSTEM WITH FREE BOUNDARY

  • Xiaohong QIN ,
  • Teng WANG ,
  • Yi WANG
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  • 1 Department of Mathematics, Nanjing University of Science and Technology, Nanjing 210094, China;
    2 Department of Mathematics, School of Science, Beijing Forestry University, Beijing 100083, China;
    3 Institute of Applied Mathematics, AMSS, CAS, Beijing 100190, China

Received date: 2015-11-04

  Revised date: 2016-01-29

  Online published: 2016-08-25

Supported by

The research of X H Qin was supported by NSFC Grant No. 11171153, the research of T Wang was supported by the Fundamental Research Funds for the Central Universities No. 2015ZCQ-LY-01 and No. BLX2015-27, and the research of Y Wang was supported by NSFC Grant No. 11322106.

Abstract

In this article, we investigate the global stability of the wave patterns with the superposition of viscous contact wave and rarefaction wave for the one-dimensional compressible Navier-Stokes equations with a free boundary. It is shown that for the ideal polytropic gas, the superposition of the viscous contact wave with rarefaction wave is nonlinearly stable for the free boundary problem under the large initial perturbations for any γ>1 with γ being the adiabatic exponent provided that the wave strength is suitably small.

Cite this article

Xiaohong QIN , Teng WANG , Yi WANG . GLOBAL STABILITY OF WAVE PATTERNS FOR COMPRESSIBLE NAVIER-STOKES SYSTEM WITH FREE BOUNDARY[J]. Acta mathematica scientia, Series B, 2016 , 36(4) : 1192 -1214 . DOI: 10.1016/S0252-9602(16)30062-5

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