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

Xin Chen; Ana Bela Cruzeiro; Wenjie Ye; Qi Zhang

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arXiv · 2301.06490

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

Xin Chen·Ana Bela Cruzeiro·Wenjie Ye·Qi Zhang

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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.

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Xin Chen, Ana Bela Cruzeiro, Wenjie Ye, Qi Zhang. 2023-01-16. Forward-backward stochastic differential equations on tensor fields and application to Navier-Stokes equations on Riemannian manifolds. https://arxiv.org/abs/2301.06490

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