Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system

Abstract

The inviscid 2D Boussinesq system with thermal diffusivity and multiplicative noise of transport type is studied in the $L^2$-setting. It is shown that, under a suitable scaling of the noise, weak solutions to the stochastic 2D Boussinesq equations converge weakly to the unique solution of the deterministic viscous Boussinesq system. Consequently, the transport noise asymptotically regularizes the inviscid 2D Boussinesq system and enhances dissipation in the limit.

19 pages

References in corpus (3)

• Global L_2-solutions of stochastic Navier-Stokes equations
• High mode transport noise improves vorticity blow-up control in 3D Navier-Stokes equations
• Stochastic mSQG equations with multiplicative transport noises: white noise solutions and scaling limit

Cited by in corpus (2)

• Scaling Limits for Stochastic SQG Equations and 2D Inviscid Critical Boussinesq Equations with Transport Noises
• Delayed blow-up by transport noise