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

Francesco de Anna, Arghir Zarnescu
2016 Communications in Mathematical Sciences  
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.
doi:10.4310/cms.2016.v14.n8.a3 fatcat:5qka4kjkend2hnifq3bvzlirb4