Global Existence for an Attraction–Repulsion Chemotaxis-Fluid System in a Framework of Besov–Morrey type

Abstract

We consider an attraction-repulsion chemotaxis model in the whole space $${\mathbb {R}}^3$$ with logistic source coupled with the incompressible Navier–Stokes equations. By means of a contraction argument, we obtain the existence and uniqueness of global mild solutions in a framework of Besov type, namely Besov spaces based on Morrey spaces. In comparison with previous results for the system dealt with, that framework provides new solutions and allows us to consider larger initial data and force classes for global existence and uniqueness. To carry out our results, we prove some essential lemmas and estimates related to the heat semigroup and continuity properties for the Bony decomposition in our setting.