Stable and unstable flow regimes for active fluids in the periodic setting

Depending on the involved physiobiological parameters, stable or unstable behavior in active fluids is observed. In this paper a rigorous analytical justification of (in-)stability within the corresponding regimes is given. In particular, occurring instability for the manifold of ordered polar states caused by self-propulsion is proved. This represents the prerequisite for active turbulence patterns as observed in a number of applications. The approach is carried out in the periodic setting and is based on the generalized principle of linearized (in)-stability related to normally stable and normally hyperbolic equilibria.