we are happy to announce the hybrid - that is, in person with online streaming - talk of the (PMS)^2 series:

Speaker: Mario Maurelli (Università di Pisa)

Title: Existence and uniqueness by Kraichnan noise for 2D Euler equations with unbounded vorticity.

Abstract: We consider the incompressible Euler equations in two or three dimensions and we show that the addition of a suitable multiplicative It\^o noise with superlinear growth prevents a smooth solution from blowing up in finite time. The result is valid for a more general hyperbolic-type SPDE. The proof is based on the Lyapunov function method.

We consider the 2D Euler equations on $\\mathbb{R}^2$ in vorticity form, with unbounded initial vorticity, perturbed by a suitable non-smooth Kraichnan transport noise, with regularity index $\\alpha\\in (0,1)$.
We show weak existence for every $\\dot{H}^{-1}$ initial vorticity. Thanks to the noise, the solutions that we construct are limits in law of a regularized stochastic Euler equation and enjoy an additional $L^2([0,T];H^{-\\alpha})$ regularity.
For every $p>3/2$ and for certain regularity indices $\\alpha \\in (0,1/2)$ of the Kraichnan noise, we show also pathwise uniqueness for every $L^p$ initial vorticity. This result is not known without noise.
Joint work with Michele Coghi.

Date and time: Tuesday 10 October, 14:30-15:30 (Rome time zone).

Place: Aula Seminari - III piano (third floor), Dipartimento di Matematica, Politecnico di Milano, 

Piazza Leonardo da Vinci, 32 – 20133 Milano - Ed. 14 “Nave” Campus Bonardi.

Zoom link:

This is a talk of the (PMS)^2: Pavia-Milano Seminar series on Probability and Mathematical Statistics organized jointly by the universities Milano-Bicocca, Pavia and Milano-Politecnico.
The organizers (Carlo Orrieri, Maurizia Rossi, Margherita Zanella)