2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/56699We 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.46 PagesMathematical PhysicsAnalysis of PDEs60J60, 60H10, 35Q30, 58G03, 76M35text