Stochastic Differential Geometry and the Random Flows of Viscous and Magnetized Fluids in Smooth Manifolds and Eulcidean Space
Rapoport, Diego L.
arXiv, 0012032 / Harvested from arXiv
Text on arXiv
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.
Publié le : 2000-12-15
Classification:  Mathematical Physics,  Mathematics - Analysis of PDEs,  60J60, 60H10, 35Q30, 58G03, 76M35 
@article{0012032,
     author = {Rapoport, Diego L.},
     title = {Stochastic Differential Geometry and the Random Flows of Viscous and
  Magnetized Fluids in Smooth Manifolds and Eulcidean Space},
     journal = {arXiv},
     volume = {2000},
     number = {0},
     year = {2000},
     language = {en},
     url = {http://dml.mathdoc.fr/item/0012032}
}

Rapoport, Diego L. Stochastic Differential Geometry and the Random Flows of Viscous and
  Magnetized Fluids in Smooth Manifolds and Eulcidean Space. arXiv, Tome 2000 (2000) no. 0, . http://gdmltest.u-ga.fr/item/0012032/