Regularization by noise for systems of reaction-diffusion equations

Antonio Agresti (TU Delft)

Feb 15. 2024, 14:45 — 15:25

Reaction-diffusion equations arise in several physical and engineering applications as they can be used to model many physical systems such as chemical reactions. It is known that strong solutions of reaction-diffusion equations may blow-up in finite time in general. Moreover, for many system of practical interests, establishing whether the blow-up occurs or not is an open question. In this talk we show that a suitable multiplicative noise of transport type improves this situation considerably. More precisely, we show that a sufficiently intense noise ensures the existence of strong solutions on a given finite time interval. Global existence can be obtained under additional structural assumptions. Finally, an enhanced diffusion effect is also established. The arguments combine recent developments in the context of regularization by noise and in the L^p(L^q)-approach to stochastic PDEs.

Further Information
Venue:
ESI Boltzmann Lecture Hall
Recordings:
Recording
Associated Event:
Stochastic Partial Differential Equations (Workshop)
Organizer(s):
Sandra Cerrai (U of Maryland)
Martin Hairer (Imperial College London)
Carlo Marinelli (University College London)
Eulalia Nualart (U of Barcelona)
Luca Scarpa (Politecnico Milano)
Ulisse Stefanelli (U of Vienna)