AbstractInterfacial instabilities are prevalent in nature and engineering. In this talk, I will discuss the dynamics of a interface in a Hele-Shaw cell under an electric field. The coupling of the hydraulic and electric fields make the dynamics of the interface very complicated. We develop an efficient algorithm to investigate the nonlinear dynamics of the interface. Our nonlinear results revea...
AbstractWe show a Liouville type result for harmonic maps from a manifold with nonnegative Ricci curvature into positively curved target under the condition that the maps have some growth condition. Our result can be interpreted as an improved version of Choi's classical work. Moreover, Schoen-Uhlenbeck's example shows that our growth condition is almost sharp. The proof relies on Ecker-Huisken...