三维随机Navier-斯托克斯方程的Markov选择

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.

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…

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.

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。