Global existence of solutions of the liquid crystal flow for the Oseen-Frank model in \(\mathbb R^2\) (Q456759)

The authors consider two problems. First, they show global in time existence of a weak solution to the liquid crystal flow for the Oseen-Frank model. The solution is actually smooth except for finite number of singularities in time-space.NEWLINENEWLINEIn the second part they consider the Ericksen-Leslie system, i.e. a system of partial differential equations where the Navier-Stokes equations are coupled with the liquid crystal flow. For a general Oseen-Frank model (in two dimensions) they construct global in time weak solutions which are smooth except for a finite number of time instants. For both problems it is shown that the singularities can be characterized by the energy concentration around these points.