Strong solutions to the Keller‐Segel system with the weak Ln /2 initial data and its application to the blow‐up rate |
| |
Authors: | Hideo Kozono Yoshie Sugiyama |
| |
Affiliation: | Department of Mathematics, Tsuda University, Tokyo 187‐8577, Japan |
| |
Abstract: | 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 Ln /2w (?n), the weak Ln /2‐space on ?n. If ‖u0‖ is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in Ln /2w (?n) stems from obtaining a self‐similar solution which does not belong to any usual Lp(?n). Furthermore, the characterization of local existence of solutions gives us an explicit blow‐up rate of ‖u (t)‖ for n /2 < p < ∞ as t → Tmax, where Tmax denotes the maximal existence time (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) |
| |
Keywords: | Keller‐Segel system global and local existence blow‐up rate weak Lp − Lq estimate |
|
|