The orientation of Liquid crystal molecules has their preferable direction and exhibits an optical structure. Liquid crystal can also been viewed as an intermediate state between the liquid and the solid states. Given the importance, people have studied liquid crystals from the view point of modeling, computation, analysis, and engineering. In this talk, I will focus on the hydrodynamics of nematic liquid crystals, namely the Ericksen-Leslie system in conjunction with the (static) Oseen-Frank theory. The governing equation can be viewed as a strong coupling system between the forced Navier-Stokes equation for the underlying fluid velocity and the transported harmonic map heat flow to the unit sphere. I will describe some recent work on the existence of global solutions that may exhibit singularities, and the development of finite time singularity in dimensions two and three.
王长友教授，于1996年在美国Rice大学获得博士学位，先后在芝加哥大学，卡塔基大学，普渡大学工作。研究兴趣包括偏微分方程、几何分析等，曾获海外杰青项目资助（杰青B类）以及主持多项美国自然科学基金。获得荣誉包括：Sloan论文奖，美国数学会Centennial Fellowship，IMA New Directions奖，Simons Fellowship等。