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 

机构地区：[1]Institute of Applied Physics and Computational Mathematics,Beijing 100088,P.R.China [2]School of Mathematical Sciences,Peking University,Beijing 100871,P.R.China

出　　处：《Acta Mathematica Sinica,English Series》2022年第2期311-330,共20页数学学报（英文版）

基　　金：Supported by the National Natural Science Foundation of China(Grant No.12071043);the National Key Research and Development Program of China(Grant No.2020YFA0712900)。

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.

关 键 词：Critical Besov spaces chemotaxis model global well-posedness optimal time-decay rates 

分 类 号：Q141[生物学—生态学] O175[生物学—普通生物学]