We shall show an exact time interval for the existence of local strong solutions to the Keller-Segel system with the initial data u0 in L n2w (Rn), the weak L n2 -space on Rn. If ||u0||L n2 w (Rn) is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in L n2w (Rn) stems from obtaining a self-similar solution which does not belong to any usual Lp(Rn). Furthermore, the characterization of local existence of solutions gives us an explicit blow-up rate of ||u(t)||Lp(Rn) for n 2 < p≤∞as t → Tmax, where Tmax denotes the maximal existence time.
ASJC Scopus subject areas
- 数学 (全般)