Anticipating Stochastic 2D Navier-Stokes Equations

Details Anticipating Stochastic 2D Navier-Stokes Equations Anticipating Stochastic 2D Navier-Stokes Equations

2011-12-13

arxiv.org/abs/1112.2920v1

Mathematics

Analysis of PDEs

Scientific paper

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.

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