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COUPLED CHEMOTAXIS FLUID MODEL

ALEXANDER LORZ

Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Wilberforce Road, Cambridge CB3 0WA, UK

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https://doi.org/10.1142/S0218202510004507Cited by:218 (Source: Crossref)

Abstract

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 ℝ² in the case of inhomogeneous Dirichlet conditions for the oxygen.

Keywords:

AMSC: 22E46, 53C35, 57S20

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