Global existence and Asymptotic Behavior of the Solutions to Models for Chemotaxis Systems with Chemo Attractants and Repellents

We study global existence and asymptotic behavior of the solutions to models for chemotaxis systems with chemo attractants and repellents in three dimensions. Chemo attractants and repellents may be called chemo agents. For Part I, we use the logistic model for the mass. The interactions between chemo agents and the mass are taken into account. For Part II, we consider the case when mass is conserved and we use the Lotka-Volterra type model for chemo agents. To accomplish this, we use the Fourier transform and energy method. We show the existence of global solutions by the energy method. Also, we establish $L^q$ time-decay for the linear homogeneous system by using the Fourier transform and finding Green\u27s matrix. Then, we find $L^q$ time-decay for the nonlinear system using solution representation by Duhamel\u27s principle and time-weighted estimates

Existence of global solutions to chemotaxis fluid system with logistic source

We establish the existence of global solutions and L q time-decay of a three dimensional chemotaxis system with chemoattractant and repellent. We show the existence of global solutions by the energy method. We also study L q time-decay for the linear homogeneous system by using Fourier transform and finding Green’s matrix. Then, we find L q time-decay for the nonlinear system using solution representation by Duhamel’s principle and time-weighted estimate