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Large deviations principle for the stochastic vortex model

ARGOMENTI: Seminari

SEMINARI DI EQUAZIONI DIFFERENZIALI E APPLICAZIONI
Lunedi' 16 febbraio alle ore 11 in aula 1AD/30 T.A. Lorenzo Bertini (Universita' La Sapienza, Roma) terra' un seminario dal titolo "Large deviations principle for the stochastic vortex model".

-Abstract
As well known, the two dimensional Navier-Stokes equation can be formulated for the vorticity field. The so-called stochastic vortex
model is introduced by considering the vorticity concentrated in single points. In this model, the vortices evolve as independent Brownians with a mean field interaction. In the limit of infinitely many vortices one obtains, as a law of large numbers, the Navier-Stokes equation. We discuss the associated large deviations principle, in which the main technical issue is the singularity of the interaction kernel. We also briefly discuss the problem of the exit from a domain, showing that when the vorticity hits a level set of the energy it is close to a minimizer of the entropy on that level set.

Rif. int. M. Bardi, M. Novaga, A. Cesaroni

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