Solutions of equations of viscous hydrodynamics via stochastic perturbations of inviscid flows

Details Solutions of equations of viscous hydrodynamics via stochastic perturbations of inviscid flows Solutions of equations of viscous hydrodynamics via stochastic perturbations of inviscid flows

2009-08-06

arxiv.org/abs/0908.0917v1

Mathematics

Analysis of PDEs

16 pages

Scientific paper

We introduce a special stochastic perturbation of the flow of diffuse matter as a curve in the group of diffeomorphisms of flat n-dimensional torus such that the perturbed system yields a solution of Burgers equation in the tangent space at unit of the diffeomorphism group. The same perturbation of the flow of perfect incompressible fluid yields a solution of Reynolds type equation but under some special external force on the diffeomorphism group it transforms into a solution of Navier-Stokes equation without external force.

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