Global existence for an attraction-repulsion chemotaxis fluid model with logistic source

Abstract

We consider an attraction-repulsion chemotaxis model coupled with the Navier-Stokes system. This model describes the interaction between a type of cells (e.g., bacteria), which proliferate following a logistic law, and two chemical signals produced by the cells themselves that degraded at a constant rate. Also, it is considered that the chemoattractant is consumed with a rate proportional to the amount of organisms. The cells and chemical substances are transported by a viscous incompressible fluid under the influence of a force due to the aggregation of cells. We prove the existence of global mild solutions in bounded domains of \begin{document}$\mathbb{R}^N,$\end{document} \begin{document}$N = 2, 3,$\end{document} for small initial data in \begin{document}$L^p$\end{document} -spaces.