Venue
Sala Seminari
Abstract
Chemotaxis and related phenomena have been an active area of mathematical research since statistical and PDE models were first proposed by C. Patlak (’53) and E. Keller & L. Segel (’71). They are commonly studied through mean field PDE models and a common feature of these equations is the possibility of finite time blow-up under given model parameters. Recently it was shown that advection by a sufficiently strong relaxation enhancing vector field could suppress this blow up (Kiselev & Xu ’16, Iyer, Zlatos & Xu ’20). In this talk I will discuss new results (obtained with M. Tomašević) regarding criteria for the persistence of blow-up for an SPDE model of chemotaxis with stochastic advection. The noise we cover is of a form recently shown to be almost surely relaxation enhancing (Gess & Yaroslavtsev ’21) and closely related to those studied in recent works by Galeati, Flandoli and Luo.