Markov selections for the 3D stochastic Navier-Stokes equations

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dc.creatorFlandoli, F.
dc.creatorRomito, M.
dc.date2006-02-27
dc.date2007-02-05
dc.date.accessioned2026-07-07T07:44:29Z
dc.date.available2026-07-07T07:44:29Z
dc.descriptionWe investigate the Markov property and the continuity with respect to the initial conditions (strong Feller property) for the solutions to the Navier-Stokes equations forced by an additive noise. First, we prove, by means of an abstract selection principle, that there are Markov solutions to the Navier-Stokes equations. Due to the lack of continuity of solutions in the space of finite energy, the Markov property holds almost everywhere in time. Then, depending on the regularity of the noise, we prove that any Markov solution has the strong Feller property for regular initial conditions. We give also a few consequences of these facts, together with a new sufficient condition for well-posedness.
dc.description59 pages; corrected several errors and typos, added references
dc.identifierhttps://arxiv.org/abs/math/0602612
dc.identifierhttp://arxiv.org/abs/math/0602612
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/123213
dc.subjectProbability
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject76D05; 60H15, 35Q30, 60H30, 76M35
dc.titleMarkov selections for the 3D stochastic Navier-Stokes equations
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