论文标题
随机2D Inviscid Boussinesq方程与传输噪声与确定性粘性系统的收敛性
Convergence of stochastic 2D inviscid Boussinesq equations with transport noise to a deterministic viscous system
论文作者
论文摘要
在$ l^2 $ setting中研究了具有热扩散率和传输类型的乘法噪声的Inviscid 2D BoussinesQ系统。结果表明，在适当的噪声缩放下，对随机2D Boussinesq方程的弱解微弱地收敛到确定性粘性Boussinesq系统的独特解决方案。因此，转运噪声渐近地使Inviscid 2D BoussinesQ系统正规化，并在极限内增强耗散。
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.
