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
