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Asymptotic Stability of a Viscous Contact Wave for the One-Dimensional Compressible Navier-Stokes Equations for a Reacting Mixture

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Abstract

We consider the large time behavior of solutions of the Cauchy problem for the one-dimensional compressible Navier-Stokes equations for a reacting mixture. When the corresponding Riemann problem for the Euler system admits a contact discontinuity wave, it is shown that the viscous contact wave which corresponds to the contact discontinuity is asymptotically stable, provided the strength of contact discontinuity and the initial perturbation are suitably small. We apply the approach introduced in Huang, Li and Matsumura (2010) [1] and the elementary L2-energy methods.

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Acknowledgements

The author is grateful to Associate Professor Wenjun Wang for his valuable suggestions, and for many fruitful discussions on the topic of this article.

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Authors and Affiliations

  1. College of Science, University of Shanghai for Science and Technology, Shanghai, 200093, China

    Lishuang Peng

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  1. Lishuang Peng
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Correspondence to Lishuang Peng.

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This work was supported by the National Natural Science Foundation of China (11871341).

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Peng, L. Asymptotic Stability of a Viscous Contact Wave for the One-Dimensional Compressible Navier-Stokes Equations for a Reacting Mixture. Acta Math Sci 40, 1195–1214 (2020). https://doi.org/10.1007/s10473-020-0503-0

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  • DOI: https://doi.org/10.1007/s10473-020-0503-0

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