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Weak–Strong Uniqueness Property for the Full Navier–Stokes–Fourier System

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Abstract

The Navier–Stokes–Fourier system describing the motion of a compressible, viscous and heat conducting fluid is known to possess global-in-time weak solutions for any initial data of finite energy. We show that a weak solution coincides with the strong solution, emanating from the same initial data, as long as the latter exists. In particular, strong solutions are unique within the class of weak solutions.

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Authors and Affiliations

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

    Eduard Feireisl

  2. IMATH, Université du Sud Toulon-Var, BP 132, La Garde, 839 57, France

    Antonín Novotný

Authors
  1. Eduard Feireisl
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  2. Antonín Novotný
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Correspondence to Eduard Feireisl.

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Communicated by C. Dafermos

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Feireisl, E., Novotný, A. Weak–Strong Uniqueness Property for the Full Navier–Stokes–Fourier System. Arch Rational Mech Anal 204, 683–706 (2012). https://doi.org/10.1007/s00205-011-0490-3

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  • DOI: https://doi.org/10.1007/s00205-011-0490-3

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