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

Abstract

We study stochastic SQG equations on the torus 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.