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Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations

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Abstract

We consider a model of one dimensional isentropic compressible Navier–Stokes equations for which the classical Newtonian flow is replaced by a Maxwell flow. We establish the asymptotic stability of rarefaction waves for this model under some small conditions on initial perturbations and amplitude of the waves. The proof is based on \(L^2\) energy methods.

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Acknowledgements

Yuxi Hu’s research is supported by NNSFC (Grant No. 11701556) and Yue Qi Young Scholar project, China University of Mining and Technology (Beijing).

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Authors and Affiliations

  1. Department of Mathematics, China University of Mining and Technology, Beijing, 100083, People’s Republic of China

    Yuxi Hu

  2. Tianjin Binhai New Area Dagang, No. 8 Middle school, Tianjin, 300270, People’s Republic of China

    Xuefang Wang

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  1. Yuxi Hu
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Correspondence to Yuxi Hu.

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Hu, Y., Wang, X. Asymptotic Stability of Rarefaction Waves for Hyperbolized Compressible Navier–Stokes Equations. J. Math. Fluid Mech. 25, 90 (2023). https://doi.org/10.1007/s00021-023-00833-4

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