Coupled Chemotaxis Fluid Model

We consider a model system for the collective behavior of oxygen-driven swimming bacteria in an aquatic fluid. In certain parameter regimes, such suspensions of bacteria feature large-scale convection patterns as a result of the hydrodynamic interaction between bacteria. The presented model consist of a parabolic–parabolic chemotaxis system for the oxygen concentration and the bacteria density coupled to an incompressible Stokes equation for the fluid driven by a gravitational force of the heavier bacteria. We show local existence of weak solutions in a bounded domain in ℝ d , d = 2, 3 with no-flux boundary condition and in ℝ 2 in the case of inhomogeneous Dirichlet conditions for the oxygen.