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

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

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.

零粘性二维Boussinesq方程在Kraichnan传输噪声下的强唯一性

Strong Uniqueness by Kraichnan Transport Noise for the 2D Boussinesq Equations with Zero Viscosity

本文研究了无粘二维Boussinesq方程在Kraichnan型传输噪声下的强唯一性，利用噪声引起的反常正则性补偿非线性项和耦合项的奇异性，证明了概率强解的存在性与唯一性。

Limit theorems and fluctuations for point vortices of generalized Euler equations

We prove a mean field limit, a law of large numbers and a central limit theorem for a system of point vortices on the 2D torus at equilibrium with positive temperature. The point vortices are formal solutions of a class of equations generalising the Euler equations, and are also known in the literature as generalised inviscid SQG. The mean field limit is a steady solution of the equations, the CLT limit is a stationary distribution of the equations.

粗糙输运噪声扰动的二维活性标量的反常性质

Anomalous properties of 2D active scalars perturbed by rough transport noise

研究Kraichnan型粗糙输运噪声驱动的二维活性标量SPDE，证明反常正则化与可积性，并在Euler情形建立涡度反常耗散。