Turbulence in active fluids caused by self-propulsion

Article type: Research Article

Authors: Bui, Christiane^a | Löwen, Hartmut^b | Saal, Jürgen^{a; *}

Affiliations: [a] Mathematisches Institut, Angewandte Analysis, Heinrich-Heine-Universität Düsseldorf, Germany. E-mails: christiane.bui@hhu.de, juergen.saal@hhu.de | [b] Institut für Theoretische Physik II – Soft Matter, Heinrich-Heine-Universität Düsseldorf, Germany. E-mail: hlowen@hhu.de

Correspondence: [*] Corresponding author: Jürgen Saal, Heinrich-Heine-Universität Düsseldorf, Mathematisches Institut, Angewandte Analysis, 40204 Düsseldorf, Germany. Tel.: +49 211 81-11366; E-mail: juergen.saal@hhu.de.

Abstract: A rigorous analytical justification of turbulence observed in active fluids and caused by self-propulsion is presented. We prove existence of unstable wave modes for the generalized Stokes and Navier–Stokes systems by developing an approach in spaces of Fourier transformed Radon measures.

Keywords: Living fluids, active turbulence, generalized Navier–Stokes equations, well-posedness, stability

DOI: 10.3233/ASY-181510

Journal: Asymptotic Analysis, vol. 113, no. 4, pp. 195-209, 2019