Patricia Bauman, Purdue University, Dept. of Mathematics, West Lafayette, IN
Authors: Patricia Bauman and Daniel Phillips
2022 AWM Research Symposium
Analysis of Partial Differential Equations in Memory of David R. Adams
We analyze minimizers for the Landau-de Gennes $Q$-tensor energy in a three-dimensional slab, $D=U x (-a,a)$, where $U$ is a bounded simply connected domain in the plane . The minimizers are subject to tangential boundary conditions on the top and bottom faces and prescribed boundary conditions on the lateral surface. Minimizers of this energy describe stable nematic liquid crystal materials in this domain. We analyze their structure, including the location and nature of their defects, and how these features depend on the Landau-de Gennes parameter and the slab thickness.