Uniform in time $L^{\infty }$-estimates for an attraction-repulsion chemotaxis system with double saturation

Abstract

In this paper we focus on an attraction-repulsion chemotaxis model with consumed signals, formulated in bounded and smooth domains $\Omega$ of ${\mathbb{R}}^n$, with $n\ge 2$. We derive sufficient conditions on its data yielding global and bounded classical solutions to the related zero-flux Cauchy problem.