Orateur
Piotr Biler
Description
We discuss existence of radially symmetric solutions (evolution and self-similar cases) of the minimal Keller-Segel system in $\mathbb R^d$:
$$u_t=\Delta u- \nabla\cdot(u\nabla v),$$
$$\Delta v+u=0,$$
under optimal assumptions on the initial data u0 = u(0; :).
We are interested, in particular, in minimal regularity assumptions imposed on the initial data in order to a local-in-time solution does exist, as well as size conditions for (approximate) dichotomy: global-in-time existence versus finite time blowup of solutions.