Anticipating Stochastic 2D Navier-Stokes Equations
Analysis of PDEs
2011-12-14 v1 Probability
Abstract
In this article, we consider the two-dimensional stochastic Navier-Stokes equation (SNSE) on a smooth bounded domain, driven by affine-linear multiplicative white noise and with random initial conditions and Dirichlet boundary conditions. The random initial condition is allowed to anticipate the forcing noise. Our main objective is to prove the existence of a solution to the SNSE under sufficient Malliavin regularity of the initial condition. To this end we employ anticipating calculus techniques.
Cite
@article{arxiv.1112.2920,
title = {Anticipating Stochastic 2D Navier-Stokes Equations},
author = {Salah Mohammed and Tusheng Zhang},
journal= {arXiv preprint arXiv:1112.2920},
year = {2011}
}