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Compressible fluids driven by stochastic forcing: the relative energy inequality and applications. (English) Zbl 1362.35228

The relative energy inequality is shown for the compressible Navier-Stokes system driven by a stochastic forcing. The weak-strong uniqueness property for solutions (both pathwise and in law) is proved. This is a Yamabe-Watanabe type result, that is, pathwise weak-strong uniqueness implies weak-strong uniqueness in law.

MSC:

35Q35 PDEs in connection with fluid mechanics
76N10 Existence, uniqueness, and regularity theory for compressible fluids and gas dynamics
60H15 Stochastic partial differential equations (aspects of stochastic analysis)
76M35 Stochastic analysis applied to problems in fluid mechanics
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