Scaling Limits for Stochastic SQG Equations and 2D Inviscid Critical Boussinesq Equations with Transport Noises

Abstract

We study stochastic SQG equations on the torus ${\mathbb{T}}^2$ with multiplicative transport noise in the $L^2$-setting. Under a suitable scaling of the noise, we show that the solutions converge weakly to the unique solution to the deterministic dissipative SQG equation. A similar scaling limit result is proved also for the stochastic 2D inviscid critical Boussinesq equations.

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References in corpus (2)

• Global well-posedness for the critical 2D dissipative quasi-geostrophic equation
• Global L_2-solutions of stochastic Navier-Stokes equations