Chemotaxis and related phenomena have been an active area of mathematical research since statistical and PDE models were first proposed by C. Patlak (\u201953) and E. Keller & L. Segel (\u201971). 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 \u201916, Iyer, Zlatos & Xu \u201920). In this talk I will discuss new results (obtained with M. Toma\u0161evi\u0107) 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 \u201921) and closely related to those studied in recent works by Galeati, Flandoli and Luo.<\/p>\n","protected":false},"excerpt":{"rendered":"
Chemotaxis and related phenomena have been an active area of mathematical research since statistical and PDE models were first proposed…<\/p>\n