The Navier-Stokes-α equation via forward-backward stochastic differential systems

2016/10/28 by Shuai Liu, Guoping Liu, Liu, Guoping
Economics, Econometrics and Finance · Engineering · Mathematics · #FOS: Mathematics #Navier-Stokes equation solutions #Probability (math.PR) #Stability and Controllability of Differential Equations #Stochastic processes and financial applications #math.PR

paper · pdf · doi:10.48550/arxiv.1610.09421

arxiv created 2016/10/28 · openalex publication_date 2016/10/28 · arxiv updated 2016/11/01 · openalex created_date 2016/11/11 · openalex updated_date 2026/07/28

Abstract

In this paper, we use forward-backward stochastic differential systems to study the solution of two and d dimensional (d≥ 3) Navier-Stokes-α equation. For the two dimensional Navier-Stokes-α 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 (d≥ 3) case, we prove the local existence and uniqueness of the solution in Sobolev space.

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