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.”
2021
Settore MAT/06 - Probabilita' e Statistica Matematica
2D Euler equations; 2D Navier–Stokes equations; Scaling limit; Transport noise; Vorticity
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11384/110178
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