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Diego L. Rapoport

Martingale problem approach to the representations of the Navier-Stokes equations on smooth-boundary manifolds and semispace

We present the random representations for the Navier-Stokes vorticity equations for an incompressible fluid in a smooth manifold with smooth boundary and reflecting boundary conditions for the vorticity. We specialize our constructions to R ⁿ⁻¹ × R ₊ . 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.

Random Operators and Stochastic Equations, Walter de Gruyter

Print ISSN: 0926-6364
Volume: 11, 06/2003
Pages: 109 - 136

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