A Stochastic Representation for Backward Incompressible Navier-Stokes Equations

Martingale solutions for the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Levy processes

In this paper, the three-dimensional stochastic nonhomogeneous incompressible Navier-Stokes equations driven by Lévy process consisting of the Brownian motion, the compensated Poisson random measure and the Poisson random measure are considered in a bounded domain. We obtain the existence of martingale solutions. The construction of the solution is based on the classical Galerkin approximation method, stopping time, the compactness method and the Jakubowski-Skorokhod theorem.

A probabilistic representation of solutions of the incompressible Navier-Stokes equations in R3

A new probabilistic representation is presented for solutions of the incompressible Navier-Stokes equations in 3 dimensions with given forcing and initial velocity. This representation expresses solutions as scaled conditional expectations of functionals of a Markov process indexed by the nodes of a binary tree. It gives existence and uniqueness of weak solutions for all time under relatively simple conditions on the forcing and initial data. These conditions involve comparison of the forcing and initial data with majorizing kernels.

Navier-Stokes equations and forward-backward SDEs on the group of diffeomorphisms of a torus

We establish a connection between the strong solution to the spatially periodic Navier-Stokes equations and a solution to a system of forward-backward stochastic differential equations (FBSDEs) on the group of volume-preserving diffeomorphisms of a flat torus. We construct representations of the strong solution to the Navier-Stokes equations in terms of diffusion processes.

随机可压缩Navier-Stokes方程的耗散测度值解与无粘不可压缩极限

Dissipative Measure Valued Solutions to the Stochastic Compressible Navier-Stokes Equations and Inviscid-Incompressible Limit

本文提出随机可压缩Navier-Stokes方程的耗散测度值鞅解，建立相对能量不等式，证明路径wise弱-强唯一性，并研究无粘不可压缩极限。

Forward-backward stochastic differential equations on tensor fields and application to Navier-Stokes equations on Riemannian manifolds

In this paper we introduce a class of forward-backward stochastic differential equations on tensor fields of Riemannian manifolds, which are related to semi-linear parabolic partial differential equations on tensor fields. Moreover, we will use these forward-backward stochastic differential equations to give a stochastic characterization of incompressible Navier-Stokes equations on Riemannian manifolds, where some extra conditions used in [22] are not required.

A lattice gas model for the incompressible Navier-Stokes equation

We recover the Navier-Stokes equation as the incompressible limit of a stochastic lattice gas in which particles are allowed to jump over a mesoscopic scale. The result holds in any dimension assuming the existence of a smooth solution of the Navier-Stokes equation in a fixed time interval. The proof does not use non-gradient methods or the multi-scale analysis due to the long range jumps.