Contents Online
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
DOI: https://dx.doi.org/10.4310/CMS.2016.v14.n8.a3
Authors
Abstract
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.
Keywords
nematic liquid crystal fluids, Navier–Stokes equations, global wellposedness
2010 Mathematics Subject Classification
35Q30, 76A05, 76A15
Published 26 October 2016