Analysis of a Living Fluid Continuum Model

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.