Existence of stationary point vortices solution to the damped and stochastically driven Euler’s equation on the two dimensional torus is proved, by taking limits of solutions with finitely many vortices. A central limit scaling is used to show in a similar manner the existence of stationary solutions with white noise marginals.
"Stationary solutions of damped stochastic 2-dimensional Euler’s equation." Electron. J. Probab. 25 1 - 24, 2020. https://doi.org/10.1214/20-EJP474