arXiv subjects

Diego L. Rapoport

Publications and source records attributed to Diego L. Rapoport.

2 recordsLinked to original sources

arXiv2002

Martingale Problem Approach to the Representations of the Navier-Stokes Equations on Smooth Manifolds with Smooth Boundary

WE PRESENT THE RANDOM REPRESENTATIONS FOR THE NAVIER-STOKES VORTICITY EQUATIONS FOR AN INCOMPRESSIBLE FLUID IN A SMOOTH MANIFOLD WITH BOUNDARY AND REFLECTING BOUNDARY CONDITIONS FOR THE VORTICITY. WE SPECIALIZE OUR CONSTRUCTIONS TO R(n-1)xR+. WE EXTEND THESE CONSTRUCTIONS TO GIVE THE RANDOM REPRESENTATIONS FOR THE KINEMATIC DYNAMO PROBLEM OF MAGNETOHYDRODYNAMICS. WE CARRY OUT THESE INTEGRATIONS THROUGH THE APPLICATION OF THE METHODS OF STOCHASTIC DIFFERENTIAL GEOMETRY, I.E. THE GAUGE THEORY OF DIFFUSION PROCESSES ON SMOOTH MANIFOLDS.

math-ph↗

arXiv2000

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

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.

math-ph↗