John Ball

Heriot-Watt University, Edinburgh

Axisymmetry of critical points of the Onsager functional for liquid crystals

The talk will discuss critical points of the Onsager functional for liquid crystals, giving in particular a simple proof of their axisymmetry in the case of the Maier–Saupe molecular interaction, a classical result of Fatkullin & Slastikov (2005) and Liu, Zhang & Zhang (2005). The proof avoids spherical polar coordinates, instead using an integral identity on the sphere. The connection with the singular potential of Majumdar and the author for the Maier–Saupe interaction is addressed. For general molecular interactions the smoothness of critical points is proved, and for a wide class of interactions the existence of non-axisymmetric critical points established.