Stochastic Differential Geometry and the Random Flows of Viscous and Magnetized Fluids in Smooth Manifolds and Eulcidean Space

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dc.creatorRapoport, Diego L.
dc.date2000-12-15
dc.date.accessioned2026-07-07T04:28:12Z
dc.date.available2026-07-07T04:28:12Z
dc.descriptionWe 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.
dc.description46 Pages
dc.identifierhttps://arxiv.org/abs/math-ph/0012032
dc.identifierhttp://arxiv.org/abs/math-ph/0012032
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/56699
dc.subjectMathematical Physics
dc.subjectAnalysis of PDEs
dc.subject60J60, 60H10, 35Q30, 58G03, 76M35
dc.titleStochastic Differential Geometry and the Random Flows of Viscous and Magnetized Fluids in Smooth Manifolds and Eulcidean Space
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