Surface Quasi-Geostrophic Equation driven by Space-Time White Noise

Maximal inequalities and exponential estimates for stochastic convolutions driven by Lévy-type processes in Banach spaces with application to stochastic quasi-geostrophic equations

We present remarkably simple proofs of Burkholder-Davis-Gundy inequalities for stochastic integrals and maximal inequalities for stochastic convolutions in Banach spaces driven by Lévy-type processes. Exponential estimates for stochastic convolutions are obtained and two versions of Itô's formula in Banach spaces are also derived. Based on the obtained maximal inequality, the existence and uniqueness of mild solutions of stochastic quasi-geostrophic equation with Lévy noise is established.

表面准地转方程解的法律非唯一性：线性乘性噪声情形

Non-uniqueness in law of the surface quasi-geostrophic equations: the case of linear multiplicative noise

本文研究线性乘性噪声驱动的表面准地转方程，通过凸积分技术并利用剪切流关键观察与随机交换子误差改写，证明了其法律非唯一性。

受时空白噪声导数扰动的表面准地转方程

Surface quasi-geostrophic equation perturbed by derivatives of space-time white noise

该研究针对受时空白噪声导数扰动的奇异表面准地转方程，通过改进的Da Prato--Debussche技巧与凸积分迭代，首次证明了次临界、临界及超临界情形下无穷多非高斯概率强解和遍历平稳解的存在性。

随机双层准地转模型的指数遍历性

Exponential ergodicity for a stochastic two-layer quasi-geostrophic model

本文研究了受加性噪声扰动的双层准地转模型，克服了随机强迫仅作用于顶层导致的空间退化噪声挑战，证明了解分布向不变测度的指数收敛性，并为耗散 SPDE 提供了广义耦合技术的通用框架。

Fractionally dissipative stochastic quasi-geostrophic type equations on $R^d$

Stochastic fractionally dissipative quasi-geostrophic type equation on $R^d$ with a multiplicative Gaussian noise is considered. We prove the existence of a martingale solution. In the 2D sub-critical case we prove also the pathwise uniqueness of the solutions.

Sub and supercritical stochastic quasi-geostrophic equation

In this paper, we study the 2D stochastic quasi-geostrophic equation on $\mathbb{T}^2$ for general parameter $α\in(0,1)$ and multiplicative noise. We prove the existence of weak solutions and Markov selections for multiplicative noise for all $α\in(0,1)$. In the subcritical case $α>1/2$, we prove existence and uniqueness of (probabilistically) strong solutions. Moreover, we prove ergodicity for the solution of the stochastic quasi-geostrophic equations in the subcritical case driven by possibly degenerate noise. The law of large numbers for the solution of the stochastic quasi-geostrophic equa…

随机无粘多层准地转方程不变测度的存在性

Existence of Invariant Measures for Stochastic Inviscid Multi-Layer Quasi-Geostrophic Equations

该研究针对二维有界域内带随机强迫的无粘三层准地转模型，在正则性假设下确立系统适定性，并借助改进的Krylov-Bogoliubov方法证明了有界函数支集上不变测度的存在性。

Stochastic quasi-geostrophic equation

In this note we study the 2d stochastic quasi-geostrophic equation in $\mathbb{T}^2$ for general parameter $α\in (0,1)$ and multiplicative noise. We prove the existence of martingale solutions and pathwise uniqueness under some condition in the general case, i.e. for all $α\in (0,1)$. In the subcritical case $α>1/2$, we prove existence and uniqueness of (probabilistically) strong solutions and construct a Markov family of solutions. In particular, it is uniquely ergodic for $α>2/3$ provided the noise is non-degenerate. In this case, the convergence to the (unique) invariant measure is exponent…

关于由一般加性噪声驱动的表面准地转方程的凸积分解

On convex integration solutions to the surface quasi-geostrophic equation driven by generic additive noise

本文利用凸积分方法研究一般加性噪声驱动的表面准地转方程，在随机卷积满足正则性条件时证明弱解存在，并表明解线性受控于随机卷积，从而无需依赖噪声的高斯性、马尔可夫性或鞅性质即可推导解的进一步性质。

Equilibrium Statistical Mechanics of Barotropic Quasi-Geostrophic Equations

We consider equations describing a barotropic inviscid flow in a channel with topography effects and beta-plane approximation of Coriolis force, in which a large-scale mean flow interacts with smaller scales. Gibbsian measures associated to the first integrals energy and enstrophy are Gaussian measures supported by distributional spaces. We define a suitable weak formulation for barotropic equations, and prove existence of a stationary solution preserving Gibbsian measures, thus providing a rigorous infinite-dimensional framework for the equilibrium statistical mechanics of the model.