We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport-type noises and L2-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.”
Scaling limit of stochastic 2D Euler equations with transport noises to the deterministic Navier–Stokes equations
Flandoli F.;Galeati L.;Luo D.
2021
Abstract
We consider a family of stochastic 2D Euler equations in vorticity form on the torus, with transport-type noises and L2-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.”File in questo prodotto:
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Flandoli Galeati Luo scaling limit.pdf
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