Global Fujita-Kato's Type Solutions and Long-time Behavior for the Multidimensional Chemotaxis Model

• 作者: Qiong Lei CHEN Xiao Nan HAO Jing Yue LI
• 来源期刊: 数学学报（英文版）
• 年，卷（期）: 2022,（2）
• 页码范围: 311-330
• 页数: 20页
• 语种: 英文

摘要

We establish the global well-posedness for the multidimensional chemotaxis model with some classes of large initial data,especially the case when the rate of variation of ln v0 (v0 is the chemical concentration) contains high oscillation and the initial density near the equilibrium is allowed to have large oscillation in 3D.Besides,we show the optimal time-decay rates of the strong solutions under an additional perturbation assumption,which include specially the situations of d =2,3 and improve the previous time-decay rates.Our method mainly relies on the introduce of the effective velocity and the application of the localization in Fourier spaces.