Stochastic vorticity equation: existence, uniqueness and regularity results in the flat torus and in the whole plane
Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at] unitn.it
Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"
- Margherita Zanella (Università di Pavia)
In this talk we deal with the two-dimensional stochastic Navier-Stokes equations in their vorticity form. We consider at first the equations on the flat torus, with a stochastic forcing term given by a Gaussian noise, white in time and colored in space. We prove existence and uniqueness of a weak solution process in the martingale measure approach (Walsh notion of solution). Moreover, we prove the space-time continuity of the solution process and we study its regularity in the Malliavin sense.
Then we consider the Navier-Stokes equations in vorticity form in the whole plane R2 with a white noise forcing term of multiplicative type, whose spatial covariance is not regular enough to apply the Itô calculus in Lq spaces, q>1. We prove the existence of a unique strong (in the probability sense) solution.
The talk is based on two joint works with B. Ferrario.
Referente: Stefano Bonaccorsi