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

2023/01/16 by Xin Chen, Ana Bela Cruzeiro, Chen, Xin +5
Computer Science · Economics, Econometrics and Finance · Mathematics · #58J65 #60H10 #60H30 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Numerical methods in inverse problems #Probability (math.PR) #Stochastic processes and financial applications

paper · pdf · doi:10.48550/arxiv.2301.06490

openalex publication_date 2023/01/16 · openalex created_date 2023/01/20 · openalex updated_date 2026/07/28

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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