Orateur
Description
We consider the Cauchy problem for the two-dimensional fully parabolic classical Keller–Segel system. Since its introduction in the 1970s, this system has been extensively studied from various perspectives. One of the main topics is the so-called critical mass phenomenon, namely
the $L1$ -threshold behavior in two spatial dimensions. Global existence at the critical mass has been established under radial symmetry, additional moment conditions on the initial data, or
for the parabolic-elliptic system as a simplified model. These restrictions arise because classical energy-based methods lose effectiveness at the critical level, and controlling the behavior of
solutions at spatial infinity becomes a major difficulty. However, such assumptions are extrinsic to the intrinsic scaling structure underlying the critical mass phenomenon.
In this talk, we establish global-in-time existence at the critical mass for general initial data, without any additional assumptions. The proof is based on a refined Lyapunov functional and associated dissipative estimates, which allow us to recover sufficient control of the dynamics in the whole space.