Global-in-time probabilistically strong and Markov solutions to stochastic 3D Navier--Stokes equations: existence and non-uniqueness

具无界噪声的非线性SPDE的弱解与强解

Weak and Strong Solutions to Nonlinear SPDEs with Unbounded Noise

本文为具无界噪声的非线性SPDE引入扩展变分框架，定义了三种递进强度的解及其存在性准则，并为带传输噪声及特定边界条件的Navier-Stokes方程提供了多个适定性结果。

具有 Navier 边界条件和随机 Lie 输运的 Navier-Stokes 方程：适定性与无粘极限

Navier-Stokes Equations with Navier Boundary Conditions and Stochastic Lie Transport: Well-Posedness and Inviscid Limit

本文研究二维随机 Navier-Stokes 方程在 Navier 边界条件下的全局强适定性，并证明 SALT 噪声等情形下无粘极限收敛到随机 Euler 方程弱解。

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

In this paper, we prove the existence and uniqueness of a smooth solution to a tamed 3D Navier-Stokes equation in the whole space. In particular, if there exists a bounded smooth solution to the classical 3D Navier-Stokes equation, then this solution satisfies our tamed equation. Moreover, using this renormalized equation we can give a new construction for a suitable weak solution of the classical 3D Navier-Stokes equation introduced in [Scheffer: Hausdorff measure and the Navier-Stokes equations. Comm. Math. Phys., 1977] and [Caffarelli, Kohn, Nirenberg: Partial regularity of suitable weak so…

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.

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

We reduce the construction of a weak solution of the Cauchy problem for the Navier-Stokes system to the construction of a solution to a stochastic problem. Namely, we construct diffusion processes which allow us to obtain a probabilistic representation of a weak (in distributional sense) solution to the Cauchy problem for the Navier- Stokes system.