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Nonlinear Stability of Rarefaction Waves to the Compressible Navier-Stokes Equations for a Reacting Mixture with Zero Heat Conductivity

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Abstract

In this paper, we study the time-asymptotically nonlinear stability of rarefaction waves for the Cauchy problem of the compressible Navier-Stokes equations for a reacting mixture with zero heat conductivity in one dimension. If the corresponding Riemann problem for the compressible Euler system admits the solutions consisting of rarefaction waves only, it is shown that its Cauchy problem has a unique global solution which tends time-asymptotically towards the rarefaction waves, while the initial perturbation and the strength of rarefaction waves are suitably small.

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Authors and Affiliations

  1. Faculty of Science, Beijing University of Technology, Beijing, 100124, China

    Lishuang Peng & Yong Li

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  1. Lishuang Peng
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  2. Yong Li
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Correspondence to Lishuang Peng.

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The authors declare no conflict of interest.

This work was supported by the Beijing Natural Science Foundation (1182004, Z180007, 1192001).

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Peng, L., Li, Y. Nonlinear Stability of Rarefaction Waves to the Compressible Navier-Stokes Equations for a Reacting Mixture with Zero Heat Conductivity. Acta Math Sci 43, 2179–2203 (2023). https://doi.org/10.1007/s10473-023-0515-7

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  • DOI: https://doi.org/10.1007/s10473-023-0515-7

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