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

Dominic Breit; Eduard Feireisl; Martina Hofmanová

doi:10.1007/s00220-017-2833-x

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

Dominic Breit, Eduard Feireisl, Martina Hofmanová

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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.

Original language	English
Pages (from-to)	443–473
Number of pages	31
Journal	Communications in Mathematical Physics
Volume	350
Issue number	2
Early online date	31 Jan 2017
DOIs	https://doi.org/10.1007/s00220-017-2833-x
Publication status	Published - Mar 2017

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Dominic Breit
- db13@hw.ac.uk
- School of Mathematical & Computer Sciences - Associate Professor
- School of Mathematical & Computer Sciences, Mathematics - Associate Professor
Person: Academic (Research & Teaching)

Cite this

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AB - 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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