Asymptotic dynamics for the parabolic–elliptic Keller–Segel system

par M. Federico Buseghin (Université Paris Cergy)

mardi 2 juin 2026, 14:00 → 15:00 Europe/Paris

Fokko (ICJ)

The parabolic–elliptic Keller–Segel equation in two dimensions provides a fundamental example of a critical aggregation–diffusion model describing chemotactic aggregation and exhibiting a competition between diffusion and concentration. The behavior of solutions strongly depends on the total mass with a critical threshold separating qualitatively different regimes. In this talk I will first review some classical and recent results on the asymptotic dynamics in the subcritical and supercritical regimes. I will then focus on the critical mass case where solutions exist globally but may still exhibit concentration phenomena at infinite time. The main result presented is a recent joint work with Charles Collot (CY Cergy Paris Université), where we classify the long-time dynamics of solutions with critical mass and finite second moment. I will also discuss some of the key ideas underlying the proof.