Refined temporal asymptotics near blow-up points in the planar Keller-Segel system

Frederic Heihoff, Michael Winkler

For the Keller-Segel system \[ \left\{\, \begin{aligned} u_t &= Δu - \nabla \cdot ( u \nabla v ), \\ v_t &= Δv - v + u \end{aligned} \right. \tag{$\star$} \] posed in a planar do…