The Keller-Segel system of parabolic-parabolic type in homogeneous Besov spaces framework

[摘要] We show the existence and uniqueness of local strong solutions of Keller-Segel system of parabolic parabolic type for arbitrary initial data in the homogeneous Besov space which is scaling invariant. We also construct global strong solutions for small initial data, where the solutions belong to the Lorentz space in time direction. The proof is based on the maximal Lorentz regularity theorem of heat equations. (c) 2021 Elsevier Inc. All rights reserved.

[发布日期] 2021-10-15

[关键词] Keller-Segel system;Maximal Lorentz regularity;Homogeneous Besov spaces;Scaling invariant