A closer look at Liquid Crystal Displays

Robert Lasarzik:

In every part of our life, we nowadays get in touch with liquid crystal displays. Our computers, watches, and phones contain this mysterious fluid, which is at a physical state between liquid and solid matter. To be able to keep pace with the rapid development of displays of electrical devices in recent years, a thorough theoretical understanding of the materials used in these devices is required.
In this talk, we present results concerning liquid crystals of nematic type. We rst consider the essential physical properties of such fluids and discuss the mathematical models available. We then study the governing nonlinear partial differential equations from a more mathematical point of view and discuss corresponding functional analytic techniques as well as difficulties arising. Recent theoretical results are presented.
In particular, we show existence of generalized solutions for the Ericksen-Leslie model under certain general assumptions on the free energy potential using a discrete approximation scheme. Finally, we discuss the adaption of the proof to non-nematic liquid crystal phases and other open problems.