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Communications in Mathematical Physics

, Volume 350, Issue 2, pp 443–473 | Cite as

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

  • Dominic Breit
  • Eduard FeireislEmail author
  • Martina Hofmanová
Article

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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Copyright information

© Springer-Verlag Berlin Heidelberg 2017

Authors and Affiliations

  • Dominic Breit
    • 1
  • Eduard Feireisl
    • 2
    Email author
  • Martina Hofmanová
    • 3
  1. 1.Department of MathematicsHeriot-Watt UniversityRiccarton, EdinburghScotland, UK
  2. 2.Institute of Mathematics of the Academy of Sciences of the Czech RepublicPraha 1Czech Republic
  3. 3.Institute of MathematicsTechnical University BerlinBerlinGermany

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