Markov selection for the three-dimensional stochastic Navier-Stokes equations

June 6, 2019
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Venue: Seminar Room “-1” – Department of Mathematics – Via Sommarive, 14 Povo - Trento
Time: 10.50 a.m.

  • Morena Celant - PhD in Mathematics

Abstract:

The well posedness of the 3D Navier-Stokes equations is still an open problem, both in the deterministic case and in case of stochastic perturbations. Another structural property of the stochastic differential equations, beside existence, uniqueness and continuous dependence on initial conditions, is the Markov property. When uniqueness is open, Markov property has no direct meaning but a natural question is the existence of a Markov selection.
In this talk we would like to show the existence of a Markov selection for a very large class of 3D stochastic Navier-Stokes equations by means of an abstract selection principle. To prove this fact, we need to use a definition of weak solution which incorporates a super- martingale formulation of the energy inequality. Due to the lack of continuity of trajectories of the solutions, the Markov property for selections holds only almost everywhere in time.

Supervisor: Carlo Orrieri