A Stochastic Representation for Backward Incompressible Navier-Stokes Equations

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dc.creatorZhang, Xicheng
dc.date2008-10-26
dc.date2008-11-01
dc.date.accessioned2026-07-07T10:14:18Z
dc.date.available2026-07-07T10:14:18Z
dc.descriptionBy reversing the time variable we derive a stochastic representation for backward incompressible Navier-Stokes equations in terms of stochastic Lagrangian paths, which is similar to Constantin and Iyer's forward formulations in \cite{Co-Iy}. Using this representation, a self-contained proof of local existence of solutions in Sobolev spaces are provided for incompressible Navier-Stokes equations in the whole space. In two dimensions or large viscosity, an alternative proof to the global existence is also given. Moreover, a large deviation estimate for stochastic particle trajectories is presented when the viscosity tends to zero.
dc.description17 Pages. Corrected some misprints and added a proof to the global existence for large viscosity by probability approach
dc.identifierhttps://arxiv.org/abs/0810.4664
dc.identifierhttp://arxiv.org/abs/0810.4664
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/172833
dc.subjectProbability
dc.subjectAnalysis of PDEs
dc.subject60H15, 37A25
dc.titleA Stochastic Representation for Backward Incompressible Navier-Stokes Equations
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