Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier-Stokes equations

Abstract

We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport type noises and $L^2$-initial data. Under a suitable scaling of the noises, we show that the solutions converge weakly to that of the deterministic 2D Navier--Stokes equations. Consequently, we deduce that the weak solutions of the stochastic 2D Euler equations are approximately unique and "weakly quenched exponential mixing".

26 pages

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Cited by in corpus (1)

• Coagulation dynamics under random field: turbulence effects on rain