学术讲座

报告题目：Solutions with one dimensional concentration for a two dimensional Gross-Pitaevskii model with general potential

报告专家：杨军 教授

报告时间：2026年9月17日（周四）下午16：00

报告地点：湘江楼A926会议室

报告摘要：We study a Gross-Pitaevskii equation with a trap potential under the unit mass constraint, which is used to describe Bose-Einstein condensates with attractive interaction. First, we provide some necessary conditions for the existence of a solution concentrating at a curve. Next, under stationary and non-degeneracy assumptions on the curve with respect to an auxiliary weighted length involving the trap potential, we construct a solution with concentration directed along the curve, provided that the parameter $-\lambda \to +\infty$. Our result improves upon very recent results by Q. Guo, S. Tian and Y. Zhou in Calc. Var. Partial Differential Equations (Vol. 61, 2022, no. 2), which relied heavily on the radial symmetry assumption of the trap potential. This is a joint work with Lipeng Duan and Suting Wei.

专家简介：杨军，广州大学教授，博士生导师，2007年获得香港中文大学数学哲学博士学位，师从非线性偏微分方程领域国际著名数学家魏军城教授。主要从事数学领域中非线性分析的研究，用非线性泛函分析中的变分方法、约化理论来研究具有相关应用和理论背景的非线性偏微分方程，比如物理学中描述Bose-Einstein凝聚的Gross-Pitaevskii方程，描述相变现象的Allen-Cahn方程以及具有几何背景的Shrödinger map方程和wave map方程。杨军教授在以上问题的爆破解、涡旋解、预定集中曲线/曲面解的构造等方面做出了一系列重要成果，得到国际同行的广泛引用和高度认可。主要成果发表在Geometric and Functional Analysis 、Transactions of the American Mathematical Society、Indiana University Mathematical Journa、Communications in Partial Differential Equations 、SIAM Journal on Mathematical Analysis等国际数学一流刊物上。主持国家自然科学基金青年项目1项和面上项目4项。