ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

doi:10.1016/S0252-9602(12)60025-3

数学物理学报(英文版) ›› 2012, Vol. 32 ›› Issue (1): 389-412.doi: 10.1016/S0252-9602(12)60025-3

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

Hakho Hong, Feimin Huang

Institute of Mathematics, Academy of Sciences, Pyonyang, DPR of Korea|Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2011-12-15 出版日期:2012-01-20 发布日期:2012-01-20
基金资助:
The first author’s research was partially supported by NSFC (10825102) for distinguished youth scholar. The second author’s research was supported by the CAS-TWAS postdoctoral fellowships (FR number: 3240223274) and AMSS in Chinese Academy of Sciences.

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

Hakho Hong, Feimin Huang

Institute of Mathematics, Academy of Sciences, Pyonyang, DPR of Korea|Institute of Applied Mathematics, Academy of Mathematics and System Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2011-12-15 Online:2012-01-20 Published:2012-01-20
Supported by:
The first author’s research was partially supported by NSFC (10825102) for distinguished youth scholar. The second author’s research was supported by the CAS-TWAS postdoctoral fellowships (FR number: 3240223274) and AMSS in Chinese Academy of Sciences.

摘要/Abstract

摘要：

A free boundary problem for the one-dimensional compressible Navier-Stokes equations is investigated. The asymptotic behavior of solutions toward the superposition of contact discontinuity and shock wave is established under some smallness conditions. To do this, we first construct a new viscous contact wave such that the momentum equation is satisfied exactly and then determine the shift of the viscous shock wave. By using them
together with an inequality concerning the heat kernel in the half space, we obtain the desired a priori estimates. The proof is based on the elementary energy method by the anti-derivative argument.

关键词: compressible Navier-Stokes equations, free boundary, superposition of shock wave and contact discontinuity, stability

Abstract:

Key words: compressible Navier-Stokes equations, free boundary, superposition of shock wave and contact discontinuity, stability

中图分类号:

35Q30

Hakho Hong, Feimin Huang. ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY[J]. 数学物理学报(英文版), 2012, 32(1): 389-412.

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ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

ASYMPTOTIC BEHAVIOR OF SOLUTIONS TOWARD THE SUPERPOSITION OF CONTACT DISCONTINUITY AND SHOCK WAVE FOR COMPRESSIBLE NAVIER-STOKES EQUATIONS WITH FREE BOUNDARY

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