驯服的三维Navier-斯托克斯方程：解的存在性、唯一性和正则性

Stochastic Navier--Stokes equations on a 3D thin domain

Stochastic Navier--Stokes equations in a thin three-dimensional domain are considered, driven by additive noise. The convergence of martingale solution of the stochastic Navier--Stokes equations in a thin three-dimensional domain to the unique martingale solution of the 2D stochastic Navier--Stokes equations, as the thickness of the film vanishes, is established. Hence, we justify the approximation of 3D Navier--Stokes equations driven by random forcing by its corresponding two-dimensional setting in applications.

随机阻尼二维Navier-斯托克斯方程的无粘极限

Inviscid limit of stochastic damped 2D Navier-Stokes equations

研究了随机阻尼二维Navier-斯托克斯方程的无粘极限。证明了当粘性为零时，随机阻尼Navier-斯托克斯方程的定常解收敛于随机阻尼Euler方程的定常解，涡拟能的耗散率收敛于零.特别是，这个限制服从拟能平衡。该速率是相对于随机阻尼Navier-斯托克斯方程的唯一不变测度的极限测度来计算的。

Navier-Stokes方程组和扩散过程Cauchy问题的广义解

Generalized solutions of the Cauchy problem for the Navier-Stokes system and diffusion processes

我们将Navier-Stokes方程组Cauchy问题的弱解的构造归结为随机问题的解的构造。也就是说，我们构造扩散过程，使我们能够获得一个概率表示的弱（在分布意义上）的Navier-Stokes系统的柯西问题的解决方案。

Convergence of the stochastic Navier-Stokes-$α$ solutions toward the stochastic Navier-Stokes solutions

Loosely speaking, the Navier-Stokes-$α$ model and the Navier-Stokes equations differ by a spatial filtration parametrized by a scale denoted $α$. Starting from a strong two-dimensional solution to the Navier-Stokes-$α$ model driven by a multiplicative noise, we demonstrate that it generates a strong solution to the stochastic Navier-Stokes equations under the condition $α$ goes to 0. The initially introduced probability space and the Wiener process are maintained throughout the investigation, thanks to a local monotonicity property that abolishes the use of Skorokhod's theorem. High spatial re…

Stokes、Navier-Stokes和Euler方程的拉格朗日结构

Lagrangian structures for the Stokes, Navier-Stokes and Euler equations

利用拉格朗日系统的随机嵌入，证明了Navier-Stokes方程、Euler方程和斯托克斯方程具有拉格朗日结构.这些方程与显式随机拉格朗日泛函的极值一致，即它们是[Cresson-Darses，J.Math.Phys.48，072703（2007）]意义上的随机拉格朗日系统

Approximations of Stochastic Navier-Stokes Equations

In this paper we show that solutions of two-dimensional stochastic Navier-Stokes equations driven by Brownian motion can be approximated by stochastic Navier-Stokes equations forced by pure jump noise/random kicks.

Ergodicity of the 2D Navier-Stokes Equations with Degenerate Multiplicative Noise

Consider the two-dimensional, incompressible Navier-Stokes equations on the torus We prove that the semigroup P_t generated by the solutions to stochastic Navier-stokes equations is asymptotically strong Feller. Moreover, we also prove that semigroup P_t is exponentially ergodic in some sense

Stochastic Navier-Stokes Equations and Related Models

Regularization by noise for certain classes of fluid dynamic equations, a theme dear to Giuseppe Da Prato (see G. Da Prato and A. Debussche, Ergodicity for the 3D stochastic Navier-Stokes equations, J. Math. Pures Appl., 2003), is reviewed focusing on 3D Navier-Stokes equations and dyadic models of turbulence.

二维随机Navier-斯托克斯方程的无粘极限

Inviscid Limit for 2D Stochastic Navier-Stokes equations

考虑了二维有界区域上的随机Navier-斯托克斯方程，其Navier边界条件为摩擦边界条件。我们建立了解的存在唯一性，并研究了粘性极限的消失。更准确地说，我们证明了随机Navier-斯托克斯方程的解收敛，当粘性趋于零，相应的随机欧拉方程的解。

环面上二维分数阶随机Navier-斯托克斯方程的大偏差--简证

Large deviations for 2D-fractional stochastic Navier-Stokes equation on the torus -Short Proof-

本文证明了耗散阶为$ α\in [\frac43, 2]$的二维分数阶随机Navier-斯托克斯方程的大偏差原理.

$α$ -稳定过程驱动的随机二维斯托克斯方程的不变性测度

Invariance measures of stochastic 2D Navier-Stokes equations driven by $α$-stable processes

本文证明了一般Lévy过程（特别是$α$ -稳定过程）驱动的随机二维斯托克斯方程的适定性，并得到了不变测度的存在性.

流形上的Lagrangian Navier-Stokes扩散：变分原理和稳定性

Lagrangian Navier-Stokes diffusions on manifolds: variational principle and stability

证明了流形上随机拉格朗日Navier-Stokes轨线的一个变分原理。我们研究的行为，这样的轨迹有关的稳定性以及粒子之间的旋转;二维环面的情况下进行了详细描述。

Large deviations principle for the invariant measures of the 2D stochastic Navier-Stokes equations on a torus

We prove here the validity of a large deviation principle for the family of invariant measures associated to a two dimensional Navier-Stokes equation on a torus, perturbed by a smooth additive noise.