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

2002/04/02 by Diego L. Rapoport, Rapoport, Diego L.
Mathematics · Physics and Astronomy · #35Q30 #60H10 #60H30 #60J60 #76D06 #76M35 #Analysis of PDEs (math.AP) #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #math-ph #math.AP #math.MP #msc:35Q30 #msc:60H10 #msc:60H30 #msc:60J60 #msc:76D06 #msc:76M35

paper · pdf · doi:10.48550/arxiv.math-ph/0204005

34 PAGES

arxiv created 2002/04/02 · arxiv updated 2009/11/30

Abstract

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.

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