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

Priola, Enrico; Gubinelli, Massimiliano; Flandoli, Franco

Priola, Enrico; Gubinelli, Massimiliano; Flandoli, Franco (2011), Full well-posedness of point vortex dynamics corresponding to stochastic 2D Euler equations, Stochastic Processes and their Applications, 121, 7, p. 1445-1463. http://dx.doi.org/10.1016/j.spa.2011.03.004

Type

Article accepté pour publication ou publié

External document link

http://fr.arxiv.org/abs/1004.1407

Date

2011

Journal name

Stochastic Processes and their Applications

Volume

121

Number

Publisher

Elsevier

Pages

1445-1463

Abstract (EN)

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.

Subjects / Keywords

Hormander conditions; Euler equations; Stochastic differential equations