2000/12/15 by Diego L. Rapoport, Rapoport, Diego L.
Economics, Econometrics and Finance · Mathematics · Physics and Astronomy · #35Q30 #58G03 #60H10 #60J60 #76M35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Geometric Analysis and Curvature Flows #Mathematical Physics (math-ph) #Stochastic processes and financial applications #advanced mathematical theories #math-ph #math.AP #math.MP #msc:35Q30 #msc:58G03 #msc:60H10 #msc:60J60 #msc:76M35
paper · pdf · doi:10.48550/arxiv.math-ph/0012032
46 Pages
arxiv created 2000/12/15 · openalex publication_date 2000/12/15 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We integrate in closed implicit form the Navier-Stokes equations for an incompressible fluid and the kinematical dynamo equation, in smooth manifolds and Euclidean space. This integration is carried out by applying Stochastic Differential Geometry, i.e. the gauge-theoretical formulation of Brownian motions. Non-Riemannian geometries with torsion of the trace-type are found to have a fundamental role. We prove that in any dimension other than 1, the Navier-Stokes equations can be represented as a purely diffusive process, while we can also give a random lagrangian representation for the diffusion of vorticity and velocity in terms of the non-Riemannian geometry.