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...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.展开更多
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)。
文摘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.
