A probabilistic representation for the vorticity of a 3D viscous fluid and for general systems of parabolic equations

2003/06/04 by Barbara Busnello, B. Busnello, Franco Flandoli +6 · 1 citation
Computer Science · Engineering · Mathematics · #35A20 #76D05 #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Fluid Dynamics and Turbulent Flows #Navier-Stokes equation solutions #Probability (math.PR) #math.AP #math.PR #msc:35A20 #msc:76D05

paper · pdf · doi:10.48550/arxiv.math/0306075

arxiv created 2003/06/04 · openalex publication_date 2003/06/04 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

A probabilistic representation formula for general systems of linear parabolic equations, coupled only through the zero-order term, is given. On this basis, an implicit probabilistic representation for the vorticity in a 3D viscous fluid (described by the Navier-Stokes equations) is carefully analysed, and a theorem of local existence and uniqueness is proved.

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