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On the high friction limit for the complete Euler system

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Abstract

We show that solutions of the complete Euler system of gas dynamics perturbed by a friction term converge to a solution of the porous medium equation in the high friction/long time limit. The result holds in the largest possible class of generalized solutions–the measure–valued solutions of the Euler system.

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Authors and Affiliations

  1. Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67, Praha 1, Czech Republic

    Eduard Feireisl

  2. Institute of Mathematics of Polish Academy of Sciences, Śniadeckich 8, 00-956, Warszawa, Poland

    Piotr Gwiazda

  3. Department of Mathematics, Dong-A University, Busan, 49315, Republic of Korea

    Young-Sam Kwon

  4. Institute of Applied Mathematics and Mechanics, University of Warsaw, Banacha 2, 02-097, Warsaw, Poland

    Agnieszka Świerczewska-Gwiazda

Authors
  1. Eduard Feireisl
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  2. Piotr Gwiazda
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  3. Young-Sam Kwon
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  4. Agnieszka Świerczewska-Gwiazda
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Correspondence to Agnieszka Świerczewska-Gwiazda.

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E. Feireisl: The work of E.F. was partially supported by the Czech Sciences Foundation (GAČR), Grant Agreement 21–02411S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. This work was partially supported by the Thematic Research Programme, University of Warsaw, Excellence Initiative Research University.

Y.–S. Kwon: The work of Y.–S. Kwon was partially supported by the National Research Foundation of Korea (NRF2022R1F1A1073801).

A. Świerczewska-Gwiazda: The work of A. Ś-G. and P.G. was partially supported by National Science Centre (Poland), agreement no 2021/43/B/ST1/02851.

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Feireisl, E., Gwiazda, P., Kwon, YS. et al. On the high friction limit for the complete Euler system. J. Evol. Equ. 24, 25 (2024). https://doi.org/10.1007/s00028-024-00956-9

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  • DOI: https://doi.org/10.1007/s00028-024-00956-9

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