Communications in Mathematical Sciences

Volume 14 (2016)

Number 8

Uniqueness of weak solutions of the full coupled Navier–Stokes and $Q$-tensor system in 2D

Pages: 2127 – 2178



Francesco de Anna (Institut de Mathématiques de Bordeaux, Université de Bordeaux, Talence, France)

Arghir Zarnescu (“Simion Stoilow” Institute of Mathematics of the Romanian Academy, Bucharest, Romania; and University of Sussex, Brighton, United Kingdom)


This paper is devoted to the full system of incompressible liquid crystals, as modeled in the $Q$-tensor framework. The main purpose is to establish the uniqueness of weak solutions in a two-dimensional setting, without imposing an extra regularity on the solutions themselves. This result only requires the initial data to fulfill the features which allow the existence of a weak solution. Thus, we also revisit the global existence result in dimensions two and three.


nematic liquid crystal fluids, Navier–Stokes equations, global wellposedness

2010 Mathematics Subject Classification

35Q30, 76A05, 76A15

Published 26 October 2016