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.

arXiv comment19 pages

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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