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 L2-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.
0