Stable and unstable flow regimes for active fluids in the periodic setting
- Resource Type
- Authors
- Christiane Bui; Christian Gesse; Jürgen Saal
- Source
- Nonlinear Analysis: Real World Applications. 69:103707
- Subject
- Computational Mathematics
Mathematics - Analysis of PDEs
Applied Mathematics
FOS: Mathematics
General Engineering
General Medicine
General Economics, Econometrics and Finance
Analysis
Analysis of PDEs (math.AP)
- Language
- ISSN
- 1468-1218
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, occuring 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.