We shall show the existence of a global strong solution to the semilinear Keller-Segel system in ℝn, n ≥ 3 of parabolic-parabolic type with small initial data u0 ∈ Lwn/2 (ℝn) and v0 ∈ BMO. Our method is based on the perturbation of linearization together with the Lp -L q-estimates of the heat semigroup and the fractional powers of the Laplace operator. As a by-product of our method, we shall construct a self-similar solution and prove the smoothing effect. Furthermore, the stability problem on our strong solutions will be also discussed.
ASJC Scopus subject areas
- 数学 (全般)