Existence of solutions for stochastic Euler equations is proved for the two-dimensional case. The laws of solutions of stochastic Navier-Stokes equations are shown to be relatively compact and all limit points (as the viscosity converges to zero) are laws of solutions to stochastic Euler equations.
"Stochastic Euler equations on the torus." Ann. Appl. Probab. 9 (3) 688 - 705, August 1999. https://doi.org/10.1214/aoap/1029962809