  Generalized Navier-Stokes equations which were proposed recently to describe
active turbulence in living fluids are analyzed rigorously. Results on
wellposedness and stability in the $L^2(\mathbb{R}^n)$-setting are derived. Due
to the presence of a Swift-Hohenberg term global wellposedness in a strong
setting for arbitrary initial data in $L^2_\sigma(\mathbb{R}^n)$ is available.
Based on the existence of global strong solutions, results on linear and
nonlinear (in-) stability for the disordered steady state and the manifold of
ordered polar steady states are derived, depending on the involved parameters.
