Forward-backward stochastic differential equations on tensor fields and application to Navier-Stokes equations on Riemannian manifolds
Probability
2023-01-18 v1 Analysis of PDEs
Abstract
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.
Keywords
Cite
@article{arxiv.2301.06490,
title = {Forward-backward stochastic differential equations on tensor fields and application to Navier-Stokes equations on Riemannian manifolds},
author = {Xin Chen and Ana Bela Cruzeiro and Wenjie Ye and Qi Zhang},
journal= {arXiv preprint arXiv:2301.06490},
year = {2023}
}