Existence of weak solutions to a dynamic model for smectic-A liquid crystals under undulations

Abstract

AbstractA nonlinear model due to Soddemann et al. (2004, Shear-induced undulation of smectic-A: molecular dynamics simulations vs. analytical theory. Eur. Phys. J. E., 13, 141–151) and Stewart(2007, Dynamic theory for smectic-A liquid crystals. Contin. Mech. Thermodyn., 18, 343–360) 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 3D case.