On the existence of global smooth solutions to the parabolic-elliptic Keller-Segel system with irregular initial data

Frederic Heihoff

We consider the parabolic-elliptic Keller-Segel system \[ \left\{ \begin{aligned} u_t &= Δu - χ\nabla \cdot (u \nabla v), \\ 0 &= Δv - v + u \end{aligned} \right. \tag{$\star$} \]…