Existence of global solution to a two-species Keller–Segel chemotaxis model

Abstract

In this paper, we investigate the global existence of nonnegative solutions of a two-species Keller–Segel model with Lotka–Volterra competitive source terms. By raising the regularity of a solution from [Formula: see text] to [Formula: see text], the existence and uniqueness of the classical global in time solution to this chemotaxis model is proved for any chemotactic coefficients [Formula: see text] when the space dimension is one. Furthermore, it is shown that the model has a unique classical global solution in two and three space dimensions if the chemotactic coefficients [Formula: see text] and [Formula: see text] are small as compared to the diffusion coefficient [Formula: see text] of the chemoattractant.