Global solvability of a two-species chemotaxis–fluid system with Lotka–Volterra type competitive kinetics

Abstract

In this paper, we study a two-species chemotaxis–fluid system with Lotka–Volterra type competitive kinetics in a bounded and smooth domain [Formula: see text] with no-flux/Dirichlet boundary conditions. We present the global existence of weak energy solution to a two-species chemotaxis Navier–Stokes system, and then the global weak energy solution which coincides with a smooth function throughout [Formula: see text], where [Formula: see text] represents a countable union of open intervals which is such that [Formula: see text]. In such two-species chemotaxis–fluid setting, our existence improves known blow-up prevention by logistic source to blow-up prevention by sub-logistic source, indicating standard logistic source is not the weakest damping source to prevent blow-up. This finding significantly extends previously known ones.