The Keller-Segel system of parabolic-parabolic type in Morrey space (Q1671239)

The existence of local-in-time and global solutions of the Keller-Segel system of chemotaxis in the whole space \(\mathbb R^n\) with the initial conditions in Morrey spaces is studied. The method of successive approximations, based on the estimation of the heat semigroup in the Morrey space and on the fractional power of the Laplace operator, is applied. Some of these results extend those in [\textit{P. G. Lemarié-Rieusset}, Adv. Differ. Equ. 18, No. 11--12, 1189--1208 (2013; Zbl 1284.35226)].