ISSN:
1432-0916

Source:
Springer Online Journal Archives 1860-2000

Topics:
Mathematics
,
Physics

Notes:
Abstract We consider the Navier-Stokes equation for a viscous and incompressible fluid inR 2. We show that such an equation may be interpreted as a mean field equation (Vlasov-like limit) for a system of particles, called vortices, interacting via a logarithmic potential, on which, in addition, a stochastic perturbation is acting. More precisely we prove that the solutions of the Navier-Stokes equation may be approximated, in a suitable way, by finite dimensional diffusion processes with the diffusion constant related to the viscosity. As a particular case, when the diffusion constant is zero, the finite dimensional theory reduces to the usual deterministic vortex theory, and the limiting equation reduces to the Euler equation.

Type of Medium:
Electronic Resource

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