Probability and PDEs

Partially supported by ERC Starting grant Dispeq agreement number 257293, PRIN and FIRB.

20 May 2013 - 24 May 2013

Aims

This workshop aims to bring together researchers interested in the interaction between probability and PDEs. Particular interest will be devoted to the regularizing effect that comes from both: randomization of initial data and/or introduction of noise. It is well--known that randomization of initial data allows to achieve local and global well--posedness results at lower regularity compared with the ones that one can reach by the deterministic theory. Strictly related is the question of existence of invariant measures for the corresponding PDEs.It is also well--known in the literature that noise has a strong regularizing effect on finite dimensional ODEs. For PDEs similar results are more difficult, but examples have been discovered where uniqueness of weak solutions is restored by noise, and blow-up is prevented by noise. A related problem is the selection of solutions to a deterministic problem when the noise is sent to zero. The main goal of this meeting is to disseminate information about the various recent techniques related to the aforementioned questions. This workshop is also supported by:

• ERC Starting grant Dispeq (agreement number 257293);
• FIRB 2012 "Dinamiche dispersive: Analisi di Fourier e Metodi Variazionali ;
• PRIN 2012"Problemi differenziali di evoluzione: approcci deterministici e stocastici e loro interazioni".