2020/11/24 by Matthew Rosenzweig, Rosenzweig, Matthew · 1 citation
Economics, Econometrics and Finance · Engineering · Mathematics · #Stochastic processes and financial applications #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions
paper · pdf · doi:10.48550/arxiv.2011.12180
In arXiv:1004.1407, Flandoli, Gubinelli, and Priola proposed a stochastic variant of the classical point vortex system of Helmholtz and Kirchoff in which multiplicative noise of transport-type is added to the dynamics. An open problem in the years since is to show that in the mean-field scaling regime, in which the circulations are inversely proportional to the number of vortices, the empirical measure of the system converges to a solution of a two-dimensional Euler vorticity equation with multiplicative noise. By developing a stochastic extension of the modulated-energy method of Serfaty and Duerinckx for mean-field limits of deterministic particle systems and by building on ideas introduced by the author for studying such limits at the scaling-critical regularity of the mean-field equation, we solve this problem under minimal assumptions.