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

## TL;DR

This paper proves the global existence of weak solutions for a nonlinear dynamic model of smectic-A liquid crystals that accounts for layer undulations and director-layer normal decoupling, extending previous models.

## Contribution

It introduces a new model incorporating layer undulations and director dynamics, and proves the existence of weak solutions in three dimensions.

## Key findings

- Global existence of weak solutions established
- Model captures layer undulations observed in experiments
- Decoupling of director and layer normal incorporated

## Abstract

A nonlinear model due to Soddemann et al. [37] and Stewart [38] 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.