Paths clustering and an existence result for stochastic vortex systems

We prove, via a pathwise analysis, an existence result for stochastic differential equations with singular coefficients that govern stochastic vortex systems. The techniques are self-contained and rely on careful estimates on the displacements of particles, obtained by recursively identifying “vortex clusters ” whose mutual interactions can be controlled. This provides a non trivial extension of techniques of Marchioro and Pulvirenti (7) for deterministic motion of vortices. KEY WORDS: vorticity, stochastic differential equations, non-local interaction AMS subject classification: 60H10, 60K35, 76B4