Finite-time Blowup in Chemotaxis

The Keller–Segel equation is a classical model for aggregation–diffusion phenomena and is known to admit finite-time blowup solutions in two and higher dimensions. In the last two decades, a substantial body of literature has investigated mechanisms for suppressing blowup, including the advection of strong passive or active flows, and logistic damping. In contrast, this talk focuses on the existence of finite-time blowup for three-dimensional Keller–Segel equation in the presence of relatively weak active fluid coupling or logistic damping. In both settings, the additional effects destroy the structure of the classical Keller–Segel system, rendering the standard second-moment method inapplicable. We therefore turn to a direct construction based on the stability analysis of an approximate blowup solution. This talk is based on joint papers with Zexing Li, Jiaqi Liu and Yixuan Wang.