Stable and unstable flow regimes for active fluids in the periodic setting. (February 2023)

• Record Type: Journal Article
• Authors: Bui, Christiane; Gesse, Christian; Saal, Jürgen
• Is Part Of: Nonlinear analysis. Volume 69(2023)
• Publication Date: 2023-02
• Subjects: Living fluids -- Active turbulence -- Generalized Navier–Stokes equations -- Periodic setting -- Well-posedness -- Stability; Nonlinear functional analysis -- Periodicals; Analyse fonctionnelle non linéaire -- Périodiques; Nonlinear functional analysis; Periodicals; 515.7248
• DOI: 10.1016/j.nonrwa.2022.103707
• Languages: English
• ISSNs: 1468-1218

Abstract

Abstract: 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.