On asymptotic isotropy for a hydrodynamic model of liquid crystals

Article type: Research Article

Authors: Dai, Mimi^a | Feireisl, Eduard^{b; *} | Rocca, Elisabetta^{c; d} | Schimperna, Giulio^e | Schonbek, Maria E.^f

Affiliations: [a] Department of Mathematics, University of Illinois at Chicago, 851 S. Morgan Street Chicago, IL 60607-7045, USA | [b] Institute of Mathematics of the Academy of Sciences of the Czech Republic, Žitná 25, 115 67 Praha 1, Czech Republic | [c] Weierstrass Institute for Applied Analysis and Stochastics, Mohrenstr. 39, D-10117 Berlin, Germany | [d] Dipartimento di Matematica, Università di Milano, Via Saldini 50, 20133 Milano, Italy | [e] Dipartimento di Matematica, Università di Pavia, Via Ferrata 1, I-27100 Pavia, Italy | [f] Department of Mathematics, University of California, Santa Cruz, CA 95064, USA

Correspondence: [*] Corresponding author. E-mail: [email protected].

Abstract: We study a PDE system describing the motion of liquid crystals by means of the Q-tensor description for the crystals coupled with the incompressible Navier–Stokes system. Using the method of Fourier splitting, we show that solutions of the system tend to the isotropic state at the rate (1+t)−3/2 as t→∞.

Keywords: liquid crystal, Q-tensor description, long-time behavior, Fourier splitting

DOI: 10.3233/ASY-151348

Journal: Asymptotic Analysis, vol. 97, no. 3-4, pp. 189-210, 2016