Hydrodynamics of biaxial nematic liquid crystals: biaxial limit and well-posedness
数学专题报告
报告题目(Title)：Hydrodynamics of biaxial nematic liquid crystals: biaxial limit and well-posedness
报告人(Speaker)：李思锐（贵州大学）
地点(Place)：教四楼 102
时间(Time)：2025年03月21日 周五 13:30-14:30
邀请人(Inviter)：蔡永强
报告摘要
We consider a two-tensor hydrodynamics derived from the molecular model. Firstly, we prove the existence and uniqueness of local in time smooth solutions to the two-tensor system. Secondly, starting from the two-tensor hydrodynamics, by the Hilbert expansion we formally derive its biaixal limit, i.e., the frame hydrodynamics for the biaxial nematic phase, which is a coupled system between the evolution equation of the orthonormal frame field in SO(3) and the Navier-Stokes equation. Thirdly, for the biaxial hydrodynamics described by a field of orthonormal frame, its well-posedness of smooth solutions in dimensional two and three and the global existence of weak solutions in dimensional two are shown, respectively. The uniqueness of global weak solutions is also established using the Littlewood-Paley theory. Finally, we rigorously justify the connection between the molecular-theory-based two-tensor hydrodynamics and the biaxial frame hydrodynamics. More specifically, we show the convergence of the solution to the two-tensor hydrodynamics to the solution to the frame hydrodynamics. This talk is based on joint works with Jie Xu (ICMSEC, AMSS, CAS).
主讲人简介
李思锐，贵州大学数学与统计学院教授。2015年7月于北京大学数学科学学院计算数学专业获理学博士学位，2015年9月入职贵州大学数学与统计学院，2018年至2021年在浙江大学数学科学学院基础数学方向从事博士后研究工作。研究兴趣为多尺度模型的理论与计算，在双轴液晶理论方面取得了一些成果。
