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

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

2000-12-15

arxiv.org/abs/math-ph/0012032v1

Physics

Mathematical Physics

46 Pages

Scientific paper

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.

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