Resumen de The Keller-Segel system of parabolic-parabolic type with initial data in weak $L^{n/2}(\mathbb{R}^n)$ and its application to self-similar solutions

Hideo Kozono, Yoshie Sugiyama

• 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-Lq -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.