Department of Mathematics

We consider generalized Navier Stokes equations in the periodic setting to describe the dynamics of highly concentrated bacterial suspensions in n=2 and n=3 dimensions. First, we consider stability and instability of the ordered polar states of the system, which form a manifold of equilibria. In the setting of infinite dimensional dynamical systems, we show the existence of absorbing sets of arbitrary high regularity. This leads to the existence of a global attractor that determines the long-term dynamics of the system.Joint work with Christiane Bui and Jürgen Saal.