The Navier-Stokes-$\alpha$ equation via forward-backward stochastic differential systems
Probability
2016-11-01 v1
Abstract
In this paper, we use forward-backward stochastic differential systems to study the solution of two and d dimensional () Navier-Stokes- equation. For the two dimensional Navier-Stokes- equation with space periodic boundary conditions, we derive the Feynmann-Kac formula associated with the vorticity equation and prove the global existence and uniqueness of the solution. For the d dimensional () case, we prove the local existence and uniqueness of the solution in Sobolev space.
Keywords
Cite
@article{arxiv.1610.09421,
title = {The Navier-Stokes-$\alpha$ equation via forward-backward stochastic differential systems},
author = {Guoping Liu},
journal= {arXiv preprint arXiv:1610.09421},
year = {2016}
}