A stochastic-Lagrangian approach to the naüier-Stokes equations in domains with boundary

Peter Constantin; Gautam Iyer

doi:10.1214/10-AAP731

A stochastic-Lagrangian approach to the naüier-Stokes equations in domains with boundary

Peter Constantin, Gautam Iyer

Research output: Contribution to journal › Article › peer-review

33 Scopus citations

Abstract

In this paper we deriüe a probabilistic representation of the deterministic 3-dimensional Naüier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in [Comm. Pure Appl. Math. 61 (2008) 330-345]. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One aspect highlighted by the formulation in the presence of boundaries is the nonlocal, implicit influence of the boundary üorticity on the interior fluid üelocity.

Original language	English (US)
Pages (from-to)	1466-1492
Number of pages	27
Journal	Annals of Applied Probability
Volume	21
Issue number	4
DOIs	https://doi.org/10.1214/10-AAP731
State	Published - Aug 2011

All Science Journal Classification (ASJC) codes

Statistics and Probability
Statistics, Probability and Uncertainty

Keywords

Naüier-Stokes
Probabilistic representation
Stochastic Lagrangian

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10.1214/10-AAP731

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abstract = "In this paper we deri{\"u}e a probabilistic representation of the deterministic 3-dimensional Na{\"u}ier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in [Comm. Pure Appl. Math. 61 (2008) 330-345]. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One aspect highlighted by the formulation in the presence of boundaries is the nonlocal, implicit influence of the boundary {\"u}orticity on the interior fluid {\"u}elocity.",

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AU - Iyer, Gautam

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AB - In this paper we deriüe a probabilistic representation of the deterministic 3-dimensional Naüier-Stokes equations in the presence of spatial boundaries. The formulation in the absence of spatial boundaries was done by the authors in [Comm. Pure Appl. Math. 61 (2008) 330-345]. While the formulation in the presence of boundaries is similar in spirit, the proof is somewhat different. One aspect highlighted by the formulation in the presence of boundaries is the nonlocal, implicit influence of the boundary üorticity on the interior fluid üelocity.

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KW - Probabilistic representation

KW - Stochastic Lagrangian

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A stochastic-Lagrangian approach to the naüier-Stokes equations in domains with boundary

Abstract

All Science Journal Classification (ASJC) codes

Keywords

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