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Compressible Fluids Driven by Stochastic Forcing: The Relative Energy Inequality and Applications

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Abstract

We show the relative energy inequality for the compressible Navier–Stokes system driven by a stochastic forcing. As a corollary, we prove the weak–strong uniqueness property (pathwise and in law) and convergence of weak solutions in the inviscid-incompressible limit. In particular, we establish a Yamada–Watanabe type result in the context of the compressible Navier–Stokes system, that is, pathwise weak–strong uniqueness implies weak–strong uniqueness in law.

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Authors and Affiliations

  1. Department of Mathematics, Heriot-Watt University, Riccarton, Edinburgh, EH14 4AS, Scotland, UK

    Dominic Breit

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

    Eduard Feireisl

  3. Institute of Mathematics, Technical University Berlin, Straße des 17. Juni 136, 10623, Berlin, Germany

    Martina Hofmanová

Authors
  1. Dominic Breit
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  2. Eduard Feireisl
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  3. Martina Hofmanová
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Corresponding author

Correspondence to Eduard Feireisl.

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Communicated by M. Hairer

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Breit, D., Feireisl, E. & Hofmanová, M. Compressible Fluids Driven by Stochastic Forcing: The Relative Energy Inequality and Applications. Commun. Math. Phys. 350, 443–473 (2017). https://doi.org/10.1007/s00220-017-2833-x

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  • DOI: https://doi.org/10.1007/s00220-017-2833-x

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