Cauchy problems for chemotaxis systems with chemo attractant and repellent

[摘要] We study the existence of global solutions and their asymptotic behavior for a chemotaxis system with chemo-attractant and repellent in three dimensions. To accomplish this, we use the Fourier transform and energy method. First, we establish Lq time-decay for the linear homogeneous system using Fourier transform and finding Green's matrix. Then, we find Lq time-decay for the nonlinear system using the Duhamel's principle and the time-weighted estimates.

[学科分类] 数学（综合）

[关键词] Energy method;a priori estimates;Fourier transform;time-decay rates.