桂贵龙教授学术报告
邀请人：李沁峰
报告时间：2022年7月26日（星期二）下午3:00-4:00
报告地点：湖南大学数学院425报告厅
题目：Semiclassical limit of Gross-Pitaevskii equation with Dirichlet boundary condition
摘要：In this talk, we justify the semiclassical limit of Gross-Pitaevskii equation with Dirichlet boundary condition on the 3-D upper space under the assumption that the leading order terms to both initial amplitude and initial phase function are sufficiently small in some high enough Sobolev norms. We remark that the main difficulty of the proof lies in the fact that the boundary layer appears in the leading order terms of the amplitude functions and the gradient of the phase functions to the WKB expansions of the solutions. In particular, we partially solved the open question proposed in [Chiron and Rousset2009, Pham, Nore and Brachet2005] concerning the semiclassical limit of Gross-Pitaevskii equation with Dirichlet boundary condition. This is a joint work with Prof. Ping Zhang.
报告人简介：桂贵龙，湘潭大学数学与计算科学学院教授，博士生导师。2010年毕业于中国科学院数学与系统科学研究院数学研究所，基础数学专业。2011年获第十届中国数学会钟家庆数学奖。主要研究流体力学方程组的数学理论，论文发表在CPAM, CMP, ARMA, Adv. Math., CPDE, JMPA, JFA等国际数学杂志。
