Invariant measure for the stochastic Navier-Stokes equations in unbounded 2D domains

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.

驯服的三维Navier-斯托克斯方程：解的存在性、唯一性和正则性

Tamed 3D Navier-Stokes Equation: Existence, Uniqueness and Regularity

本文证明了三维Navier-斯托克斯方程在全空间上光滑解的存在唯一性。特别地，如果经典的三维Navier-斯托克斯方程存在有界光滑解，则该解满足我们的方程。此外，利用这个重整化方程，我们还可以构造出在Hausdorff测度和Navier-Stokes方程中引入的经典三维Navier-Stokes方程的适当弱解.通信数学物理，1977]和[Caffarelli，Kohn，Nirenberg：Partial regularity of suitable弱解of the Navier-斯托克斯方程.通信纯应用数学，1982年]。

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.

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…

Stochastic Navier-Stokes Equations in Unbounded Channel Domains

In this paper we prove the existence and uniqueness of path-wise strong solution to stochastic viscous flow in unbounded channels with multiple outlets using local monotonicity arguments. We devise a construction for solvability using a stochastic basic vector field.

Inviscid limit of stochastic damped 2D Navier-Stokes equations

We consider the inviscid limit of the stochastic damped 2D Navier- Stokes equations. We prove that, when the viscosity vanishes, the stationary solution of the stochastic damped Navier-Stokes equations converges to a stationary solution of the stochastic damped Euler equation and that the rate of dissipation of enstrophy converges to zero. In particular, this limit obeys an enstrophy balance. The rates are computed with respect to a limit measure of the unique invariant measure of the stochastic damped Navier-Stokes equations.

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。

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

Inviscid Limit for 2D Stochastic Navier-Stokes equations

We consider stochastic Navier-Stokes equations in a 2D-bounded domain with the Navier with friction boundary condition. We establish the existence and the uniqueness of the solutions and study the vanishing viscosity limit. More precisely, we prove that solutions of stochastic Navier-Stokes equations converge, as the viscosity goes to zero, to solutions of the corresponding stochastic Euler equations.