Vortex theory approach to stochastic hydrodynamics

The objective of the paper is to study a jump-diffusion type vorticity model, describing evolution of an incompressible homogeneous viscous fluid in R2R2 in terms of its rotation. The model arises from a particle systems perspective, adopted in the point vortex theory, and represents a measure-valued stochastic partial differential equation (SPDE) whose solution, under certain conditions, is an empirical process generated by a finite system of randomly moving vortices, which interact via a (regularized) logarithmic potential and are driven by suitable independent space-time Wiener processes and compensated Poisson random measure. A continuous diffusion approximation to the above vorticity model is also presented.