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

2010/04/08 by Franco Flandoli, Flandoli, F., Massimiliano Gubinelli +3 · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #60H10 #76B47 #Dynamical Systems (math.DS) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.1004.1407

openalex publication_date 2010/04/08 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

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.

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