Existence and uniqueness theorem on weak solutions to the parabolic–elliptic Keller–Segel system

In Rn (n⩾3), we first define a notion of weak solutions to the Keller–Segel system of parabolic–elliptic type in the scaling invariant class Ls(0,T;Lr(Rn)) for 2/s+n/r=2 with n/2