Organizer: Chunmei Su

Abstract:

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).
                                                     
报告人简介：

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月加入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数学理论与计算，在液晶不同层次模型的关系方面取得了一些成果。