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Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System

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Abstract

We are concerned with the large-time behavior of solutions of the Cauchy problem to the one-dimensional compressible Navier–Stokes system for ideal polytropic fluids, where the far field states are prescribed. When the corresponding Riemann problem for the compressible Euler system admits the solution consisting of contact discontinuity and rarefaction waves, it is proved that for the one-dimensional compressible Navier–Stokes system, the combination wave of a “viscous contact wave”, which corresponds to the contact discontinuity, with rarefaction waves is asymptotically stable, provided the strength of the combination wave is suitably small. This result is proved by using elementary energy methods.

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Authors and Affiliations

  1. Institute of Applied Mathematics, AMSS & Hua Loo-Keng Key Laboratory of Mathematics, Chinese Academy of Sciences, 100190, Beijing, People’s Republic of China

    Feimin Huang & Jing Li

  2. Department of Pure and Applied Mathematics, Graduate School of Information Science and Technology, Osaka University, Toyonaka, Osaka, 560-0043, Japan

    Jing Li & Akitaka Matsumura

Authors
  1. Feimin Huang
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  2. Jing Li
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  3. Akitaka Matsumura
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Correspondence to Feimin Huang.

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Communicated by T.-P. Liu

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Huang, F., Li, J. & Matsumura, A. Asymptotic Stability of Combination of Viscous Contact Wave with Rarefaction Waves for One-Dimensional Compressible Navier–Stokes System. Arch Rational Mech Anal 197, 89–116 (2010). https://doi.org/10.1007/s00205-009-0267-0

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