| Contents |
| We consider a model which was proposed to describe processes of spontaneous pattern formation in populations of swimming aerobic bacteria. This model couples the incompressible Navier-Stokes equations to two evolutionary PDEs which, besides reaction, diffusion and convection, involve nonlinear cross-diffusion of bacteria towards oxygen.
The presentation briefly addresses topics of existence theory by reporting on known well-posedness results, as well as on remaining challenges in the analysis. The main focus will then be on the question in how far the considered system is indeed able to generate structures. A partially negative answer in this direction is presented, which asserts stabilization towards spatially homogeneous equilibria in a corresponding two-dimensional initial-bounday value problem. |
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