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

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

We study stochastic SQG equations on the torus $\mathbb{T}^2$ with multiplicative transport noise in the $L^2$-setting. Under a suitable scaling of the noise, we show that the solutions converge weakly to the unique solution to the deterministic dissipative SQG equation. A similar scaling limit result is proved also for the stochastic 2D inviscid critical Boussinesq equations.

Invariant Gibbs measures of the energy for shell models of turbulence; the inviscid and viscous cases

Gaussian measures of Gibbsian type are associated with some shell models of 3D turbulence; they are constructed by means of the energy, a conserved quantity for the 3D inviscid and unforced shell model. We prove the existence of a unique global flow for a stochastic viscous shell model and a global flow for the deterministic inviscid shell model, with the property that these Gibbs measures are invariant for these flows.

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。

Inviscid Limits for a Stochastically Forced Shell Model of Turbulent Flow

We establish the anomalous mean dissipation rate of energy in the inviscid limit for a stochastic shell model of turbulent fluid flow. The proof relies on viscosity independent bounds for stationary solutions and on establishing ergodic and mixing properties for the viscous model. The shell model is subject to a degenerate stochastic forcing in the sense that noise acts directly only through one wavenumber. We show that it is hypo-elliptic (in the sense of Hormander) and use this property to prove a gradient bound on the Markov semigroup.

带输运噪声的随机无粘Leray-$α$模型：收敛速率与中心极限定理（CLT）

Stochastic inviscid Leray-$α$ model with transport noise: convergence rates and CLT

本研究针对带输运噪声的随机无粘Leray-$α$模型，证明合适噪声尺度下其弱解收敛到确定性有粘模型的唯一解，验证了输运噪声的正则化作用，并推导了对应的中心极限定理与显式收敛速率。