报告人：甄茂鼎（合肥工业大学）

邀请人：杨美华

报告时间：2023年5月17日（星期三）9:00-12:00

报告地点：科技楼南楼713室

报告题目：Free and harmonic trapped spin-1 Bose-Einstein condensates in R^3

报告摘要：In this talk, I will present our recent results on Free and harmonic trapped spin-1 Bose-Einstein condensates in R^3. Firstly, in the free case, existence and asymptotic behavior of ground states are analyzed according to the relations among mean-field interaction constant c_{0}, spin-exchange interaction constant c_{1}, the number of atoms N and the total magnetization M. Furthermore, we show that the corresponding standing wave is strongly unstable. When the atoms are trapped in a harmonic potential, we prove the existence of ground states and excited states along with some precisely asymptotics. Besides, we get that the set of ground states is stable under the associated Cauchy flow while the excited state corresponds to a strongly unstable standing wave. Our results not only show some characteristics of three-dimensional spin-1 BEC under the effect between the spin-dependent interaction and the external magnetic field, but also support some experimental observations as well as numerical results on spin-1 BEC.This is based on a joint work with Prof. Juncheng Wei, Prof. Xiao Luo and D.r. Menghui Li.

报告人简介：甄茂鼎，博士，2020年6月获华中科技大学博士学位。在非线性泛函分析，椭圆系统的正规化解等方面取得一些成果。 在“Journal d’Analyse Mathematique”、“ Journal of Differential Equations”、“The Journal of Geometric Analysis. ”、“Discrete and Continuo us Dynamical System ” 、等刊物上发表论文10余篇。主持国家自然科学基金青年基金一项。