Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:119

Article

Cruzeiro, Ana Bela^1,2  Shamarova, Evelina^1,3 

[1] Univ Lisbon, Grp Fis Matemat, PT-1649003 Lisbon, Portugal

[2] Univ Tecn Lisboa, IST, Dep Matemat, Lisbon, Portugal

[3] Univ Porto, Ctr Matemat, Oporto, Portugal

关键词: Navier-Stokes equations;    Forward-backward SDEs;    Diffeomorphism group;   

DOI  :  10.1016/j.spa.2009.09.011

来源: Elsevier

【 摘 要 】

We establish a connection between the strong solution to the spatially periodic Navier-Stokes equations and a solution to a system of forward-back ward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier-Stokes equations in terms of diffusion processes. (C) 2009 Elsevier B.V. All rights reserved.

【 授权许可】

Free