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 KozonoYoshie Sugiyama 35Q30Keller-Segel systemself-similar solutionBMO spaceweak $L^p$-spaceheat semigroup We shall show the existence of a \emph{global} strong solution to the semilinear Keller-Segel system in $\mathbb{R}^{n}$, $n \ge 3$ of \emph{parabolic-parabolic type} with small initial data $u_{0} \in L_{w}^{n/2}(\mathbb{R}^{n})$ and $v_{0} \in \mathrm{BMO}$. Our method is based on the perturbation of linearization together with the $L^{p} - L^{q}$-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. Indiana University Mathematics Journal 2008 text pdf 10.1512/iumj.2008.57.3316 10.1512/iumj.2008.57.3316 en Indiana Univ. Math. J. 57 (2008) 1467 - 1500 state-of-the-art mathematics http://iumj.org/access/