Global solvability and asymptotic behavior in a two-species chemotaxis system with Lotka–Volterra competitive kinetics

Abstract

In this work, we consider the two-species chemotaxis system with Lotka–Volterra competitive kinetics in a bounded domain with smooth boundary. We construct weak solutions and prove that they become smooth after some waiting time. In addition, the asymptotic behavior of the solutions is studied. Our results generalize some well-known results in the literature.