The fluctuation process of the stochastic point vortex model with common noise converges in distribution to the unique strong solution of a linear fluctuation SPDE with multiplicative transport noise and a conditionally Gaussian additive noise.
Mean field limit of point vortices with environmental noises to deterministic 2D Navier-Stokes equations
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We consider point vortex systems on the two dimensional torus perturbed by environmental noise. It is shown that, under a suitable scaling of the noises, weak limit points of the empirical measures are solutions to the vorticity formulation of deterministic 2D Navier-Stokes equations.
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The fluctuation behaviour of the stochastic point vortex model with common noise
The fluctuation process of the stochastic point vortex model with common noise converges in distribution to the unique strong solution of a linear fluctuation SPDE with multiplicative transport noise and a conditionally Gaussian additive noise.