Strong solutions to the Keller-Segel system with the weak Ln /2 initial data and its application to the blow-up rate
✍ Scribed by Hideo Kozono; Yoshie Sugiyama
- Publisher
- John Wiley and Sons
- Year
- 2010
- Tongue
- English
- Weight
- 249 KB
- Volume
- 283
- Category
- Article
- ISSN
- 0025-584X
No coin nor oath required. For personal study only.
✦ Synopsis
Segel system, global and local existence, blow-up rate, weak L p -L q estimate MSC (2000) 35Q30
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
is sufficiently small, then our solution exists globally in time. Our motivation to construct solutions in L n 2 w (R n ) stems from obtaining a self-similar solution which does not belong to any usual L p (R n ). Furthermore, the characterization of local existence of solutions gives us an explicit blow-up rate of u(t) L p (R n ) for n 2 < p ≤ ∞ as t → Tmax, where Tmax denotes the maximal existence time.