Analysis of a Living Fluid Continuum Model

TL;DR

This paper rigorously analyzes a generalized Navier-Stokes model for active turbulence in living fluids, establishing well-posedness, stability, and the existence of global solutions under various conditions.

Contribution

It provides the first rigorous analysis of a living fluid continuum model, including well-posedness and stability results for the generalized Navier-Stokes equations with a Swift-Hohenberg term.

Findings

Global well-posedness in strong settings for arbitrary initial data.

Stability analysis of disordered and ordered steady states.

Existence of global strong solutions under certain parameters.

Abstract

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.