Point defects in 2-D liquid crystals with a singular potential:Profiles and stability  

作　　者：Zhiyuan Geng Wei Wang 

机构地区：[1]Basque Center for Applied Mathematics,Bilbao 48009,Spain [2]School of Mathematical Sciences,Zhejiang University,Hangzhou 310058,China

出　　处：《Science China Mathematics》2024年第11期2515-2540,共26页中国科学（数学英文版）

基　　金：supported by the Basque Government through the BERC PRO-GRAMME 2022-2025 and by the Spanish State Research Agency through Basque Center for Applied Mathematics Severo Ochoa excellence accreditation SEV-2017-0718 and through Project PID2020-114189RB-I00 funded by Agencia Estatal de Investigacion(Grant No.PID2020-114189RB-I00/AEI/10.13039/501100011033);supported by National Natural Science Foundation of China(Grant Nos.11931010 and 12271476)。

摘　　要：We study radial symmetric point defects with degree k/2 in the 2-D disk or R^(2) in the Q-tensor framework with a singular bulk energy,which is defined by Bingham closure.First,we obtain the existence of solutions for the profiles of radial symmetric point defects with degree k/2 in the 2-D disk or R^(2).Then,we prove that the solution is stable for |k| = 1 and unstable for |k| > 1.Some identities are derived and utilized throughout the proof of existence and stability/instability.

关 键 词：radial symmetric point defects singular bulk potential Bingham closure STABILITY 

分 类 号：O753.2[理学—晶体学] O77