Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations
- Emmrich, Etienne
- Lasarzik, Robert
2010 Mathematics Subject Classification
- 35Q35 35K52 76A15
- Liquid crystal, smectic-A, existence, weak solution, Galerkin approximation
A nonlinear model due to Soddemann et al.  and Stewart  describing incompressible smectic-A liquid crystals under flow is studied. In comparison to previously considered models, this particular model takes into account possible undulations of the layers away from equilibrium, which has been observed in experiments. The emerging decoupling of the director and the layer normal is incorporated by an additional evolution equation for the director. Global existence of weak solutions to this model is proved via a Galerkin approximation with eigenfunctions of the associated linear differential operators in the three-dimensional case.