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Vanishing viscosity limit of the 2D micropolar equations for planar rarefaction wave to a Riemann problem

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Abstract

We are concerned with the vanishing viscosity limit of the 2D compressible micropolar equations to the Riemann solution of the 2D Euler equations which admit a planar rarefaction wave. In this article, the key point of the analysis is to introduce the hyperbolic wave, which helps us obtain the desired uniform estimates with respect to the viscosities. Moreover, the proper combining of rotation terms and damping term is also important, which contributes to closing the basic energy estimates. Finally, a family of smooth solutions for the 2D micropolar equations converging to the corresponding planar rarefaction wave solution with arbitrary strength is pursued.

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Acknowledgements

This work was supported by the Grants from NNSFC under the Contract 11731008, 11671309 and 11971359. The authors express much gratitude to Professor Huijiang Zhao for his support and his suggestion.

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Authors and Affiliations

  1. School of Mathematics and Statistics, Wuhan University, Wuhan, 430072, China

    Guiqiong Gong

  2. Computational Science Hubei Key Laboratory, Wuhan University, Wuhan, 430072, China

    Guiqiong Gong

  3. Center for Mathematical Sciences and Department of Mathematics, Wuhan University of Technology, Wuhan, 430070, China

    Lan Zhang

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  1. Guiqiong Gong
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  2. Lan Zhang
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Correspondence to Lan Zhang.

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Gong, G., Zhang, L. Vanishing viscosity limit of the 2D micropolar equations for planar rarefaction wave to a Riemann problem. Z. Angew. Math. Phys. 71, 121 (2020). https://doi.org/10.1007/s00033-020-01347-z

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  • DOI: https://doi.org/10.1007/s00033-020-01347-z

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