Axisymmetry of critical points of the Onsager functional for liquid crystals
John Ball (Heriot-Watt University, Edinburgh)
Thursday 3rd December, 2020 14:00-15:00 ZOOM (ID: 974 6061 9119)
Topic: Applied Mathematics Seminar John Ball
Start Time : Dec 3, 2020 01:50 PM
Access Passcode: See the e-mail with subject: Seminar recording password
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.