Stochastic vorticity equation: existence, uniqueness and regularity results in the flat torus and in the whole plane

24 aprile 2018
24 aprile 2018
Staff Dipartimento di Matematica

Università degli Studi Trento
38123 Povo (TN)
Tel +39 04 61/281508-1625-1701-3898-1980.
dept.math [at]

Luogo: Dipartimento di Matematica, via Sommarive, 14 - Povo (TN) - Aula Seminari "-1"
Ore: 11:45


  • 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