Energy dissipation and regularity for a coupled Navier-Stokes and Q-tensor system

Paicu, Marius and Zarnescu, Arghir (2012) Energy dissipation and regularity for a coupled Navier-Stokes and Q-tensor system. Archive for Rational Mechanics and Analysis, 203 (1). pp. 45-67. ISSN 1432-0673

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Abstract

We study a complex non-Newtonian fluid that models the flowof nematic liquid crystals. The fluid is described by a system that couples a forced Navier–Stokes system with a parabolic-type system. We prove the existence of global weak solutions in dimensions two and three.We show the existence of a Lyapunov functional for the smooth solutions of the coupled system and use cancellations that allow its existence to prove higher global regularity in dimension two. We also show the weak–strong uniqueness in dimension two.

Item Type: Article
Schools and Departments: School of Mathematical and Physical Sciences > Mathematics
Depositing User: Arghir Zarnescu
Date Deposited: 07 May 2013 09:22
Last Modified: 07 May 2013 09:22
URI: http://sro.sussex.ac.uk/id/eprint/22051
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