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

摘要

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 L-1 to L-p(p 1), the existence and uniqueness of the classical global in time solution to this chemotaxis model is proved for any chemotactic coefficients chi(1), chi(2) 0 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 chi(1) and chi(2) are small as compared to the diffusion coefficient d(3) of the chemoattractant.