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Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento Time: 10.00 a.m.

Luciano Marzufero-PhDin Mathematics

Abstract:

At first we present the 3D stochastic Navier-Stokes equation for a divergence free vector field with periodic boundary conditions, which describes a viscous, constant density, Newtonian fluid. Then we focus the attention on a finite dimensional setting that captures several features of such equation. It covers, for example, the Galerkin approximation, that will not be discussed but only introduced, whose analysis represents a main step in view of the infinite dimensional system. In particular we illustrate a number of basic facts and open problems in a simple setting where the rigor is easy to control because most of these results are a preliminary technical step for the analysis of the infinite dimensional case. More specifically, we study existence, uniqueness and the Markov property of the solution of the stochastic evolution equation.

The seminar corresponds to one first year PhD exam