# Variational and numerical analysis of a $\mathbf{Q}$-tensor model for smectic-A liquid crystals

@inproceedings{Xia2021VariationalAN, title={Variational and numerical analysis of a \$\mathbf\{Q\}\$-tensor model for smectic-A liquid crystals}, author={Jingmin Xia and Patrick E. Farrell}, year={2021} }

. We analyse an energy minimisation problem recently proposed for modelling smectic-A liquid crystals. The optimality conditions give a coupled nonlinear system of partial differential equations, with a second-order equation for the tensor-valued nematic order parameter Q and a fourth-order equation for the scalar-valued smectic density variation u . Our two main results are a proof of the existence of solutions to the minimisation problem, and the derivation of a priori error estimates for its…

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