In this talk, we study a dynamical instability of liquid crystals induced by applied magnetic fields, which is the so-called Freedericksz transition. More precisely, we show that if the magnetic field strength exceeds the threshold, any global solution to the simplified Ericksen-Leslie system subject to the magnetic field converges exponentially to a unique nontrivial equilibrium. Here we imposed certain initial and strong anchoring boundary conditions. It is also proved that below the threshold, the equilibrium of the orientation angle is the zero state. This is based on joint work with Yuan Chen and Yong Yu.
Soojung Kim obtained her Ph.D. degree from Seoul National University, South Korea in 2013 under the supervision of Ki-Ahm Lee. She is currently a postdoctoral fellow at KAIST, South Korea. Her research interests are nonlinear partial differential equations and geometrical analysis.