Communications in Mathematical Sciences
Volume 14 (2016)
Uniqueness of weak solutions of the full coupled Navier–Stokes and $Q$-tensor system in 2D
Pages: 2127 – 2178
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