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• W3154062474 abstract "We are concerned with the three dimensional incompressible Navier--Stokes equations driven by an additive stochastic forcing of trace class. First, for every divergence free initial condition in $L^{2}$ we establish existence of infinitely many global-in-time probabilistically strong and analytically weak solutions, solving one of the open problems in the field. This result in particular implies non-uniqueness in law. Second, we prove non-uniqueness of the associated Markov processes in a suitably chosen class of analytically weak solutions satisfying a relaxed form of an energy inequality. Translated to the deterministic setting, we obtain non-uniqueness of the associated semiflows." @default.
• W3154062474 created "2021-04-26" @default.
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• W3154062474 date "2021-04-20" @default.
• W3154062474 modified "2023-10-16" @default.
• W3154062474 title "Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness" @default.
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• W3154062474 doi "https://doi.org/10.48550/arxiv.2104.09889" @default.
• W3154062474 hasPublicationYear "2021" @default.
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