Abstract

Symmetry considerations, as well as compatibility with the Oseen-Frank theory, require the presence of a cubic term (involving spatial derivatives) in the Q-tensor energy functional used for describing variationally the nematics. However the presence of the cubic term makes the energy functional unbounded from below.

We propose a dynamical approach for addressing this issue, namely to consider the L^2 gradient flow generated by the energy functional and show that the energy is dynamically bounded, namely if one starts with a bounded, suitable, energy then the energy stays bounded in time. We discuss notions of suitability which are related to the preservation of a physical constraint on the eigenvalues of the Q-tensors (without using the Ball-Majumdar singular potential).

This is joint work with G. Iyer and X. Xu (Carnegie-Mellon).