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Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations

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Abstract

We prove time-asymptotic stability toward the planar rarefaction wave for the three-dimensional full, compressible Navier–Stokes equations with the heat-conductivities in an infinite long flat nozzle domain \({\mathbb{R} \times \mathbb{T}^2}\) . Compared with one-dimensional case, the proof here is based on our new observations on the cancellations on the flux terms and viscous terms due to the underlying wave structures, which are crucial for overcoming the difficulties due to the wave propagation in the transverse directions x2 and x3 and its interactions with the planar rarefaction wave in x1 direction.

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Authors and Affiliations

  1. Institute of Applied Mathematics, AMSS, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Lin-an Li

  2. School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing, 100049, People’s Republic of China

    Lin-an Li & Yi Wang

  3. College of Applied Sciences, Beijing University of Technology, Beijing, 100124, People’s Republic of China

    Teng Wang

  4. CEMS, HCMS, NCMIS, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing, 100190, People’s Republic of China

    Yi Wang

Authors
  1. Lin-an Li
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  2. Teng Wang
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  3. Yi Wang
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Correspondence to Teng Wang.

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Communicated by L. Székelyhidi

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Li, La., Wang, T. & Wang, Y. Stability of Planar Rarefaction Wave to 3D Full Compressible Navier–Stokes Equations. Arch Rational Mech Anal 230, 911–937 (2018). https://doi.org/10.1007/s00205-018-1260-2

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  • DOI: https://doi.org/10.1007/s00205-018-1260-2

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