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Statistical solutions for the Navier–Stokes–Fourier system

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Abstract

We show a general stability result in the framework of strong solutions of the Navier–Stokes–Fourier system describing the motion of a compressible viscous and heat conducting gas. As a corollary, we develop a concept of statistical solution in the class of regular solutions “beyond the blow up time”.

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Acknowledgements

The work of E.F. was partially supported by the Czech Sciences Foundation (GAČR), Grant Agreement 21–02411 S. The Institute of Mathematics of the Academy of Sciences of the Czech Republic is supported by RVO:67985840. M.L. has been funded by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation) - Project no. 233630050 - TRR 146. She is grateful to the Gutenberg Research College and Mainz Institute of Multiscale Modelling for supporting her research

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Authors and Affiliations

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

    Eduard Feireisl

  2. Institute of Mathematics, Johannes Gutenberg–University Mainz, Staudingerweg 9, 55 128, Mainz, Germany

    Mária Lukáčová-Medvid’ová

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  1. Eduard Feireisl
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Feireisl, E., Lukáčová-Medvid’ová, M. Statistical solutions for the Navier–Stokes–Fourier system. Stoch PDE: Anal Comp 12, 1021–1045 (2024). https://doi.org/10.1007/s40072-023-00298-6

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