Global strong solution to the semi-linear Keller–Segel system of parabolic–parabolic type with small data in scale invariant spaces
- Kozono, Hideo
- Sugiyama, Yoshie
Publication date
July 2009
DOI Publisher
Elsevier Inc. ISSN
0022-0396 Citation count (estimate)
21Abstract
AbstractWe shall show existence of global strong solution to the semi-linear Keller–Segel system in Rn, n⩾3, of parabolic–parabolic type with small initial data u0∈Hnr−2,r(Rn) and v0∈Hnr,r(Rn) for max{1,n/4}<r<n/2. Our method is based on the perturbation of linealization together with the Lp–Lq estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall prove the decay property of solutions as the time goes to infinity
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