Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations

STOCHASTIC PROCESSES AND THEIR APPLICATIONS

卷:121

Article

Flandoli, F.³  Gubinelli, M.^1,2  Priola, E.⁴ 

[1] Univ Paris 09, CEREMADE, F-75775 Paris 16, France

[2] Univ Paris 09, CNRS, UMR 7534, F-75775 Paris 16, France

[3] Univ Pisa, Dipartimento Matemat Applicata U Dini, I-56100 Pisa, Italy

[4] Univ Turin, Dipartimento Matemat, I-10124 Turin, Italy

关键词: Stochastic differential equations;    Euler equations;    Vortex dynamics;    Hormander conditions;   

DOI  :  10.1016/j.spa.2011.03.004

来源: Elsevier

【 摘 要 】

The motion of a finite number of point vortices on a two-dimensional periodic domain is considered. In the deterministic case it is known to be well posed only for almost every initial configuration. Coalescence of vortices may occur for certain initial conditions. We prove that when a generic stochastic perturbation compatible with the Eulerian description is introduced, the point vortex motion becomes well posed for every initial configuration, in particular coalescence disappears. (C) 2011 Elsevier B.V. All rights reserved.

【 授权许可】

Free