报告题目1：Uniqueness and cylindrical symmetry ofground states for magnetic nonlinearChoquard equation

报告人：李帅副教授，华中农业大学

报告时间：2025年11月21日（周五）14:30-15:50

报告地点：#腾讯会议：894-541-502

报告摘要：This talk focuses on ground states of the following magnetic nonlinear Choquard equation:

-Δ_Au+V(x)u=μu+(I₂*|u|²)u in R³,

Where u∈H¹(R³, C) satisfies |u|₂²=m>0, V(x)∈L^∞(R³), I₂:=1/(4π|x|) is the Riesz potential and Δ_A denotes the magnetic Laplacian. By considering the associated constrained minimization problem e_A(m), we prove the existence of ground states by employing the concentration compactness principle. Furthermore, we provide a refined description of the asymptotic behavior of ground states as m→∞ by establishing the expansion of e_A(m) up to the second order. Additionally, we conclude that, there exists a unique ground state (up to a constant phase), which must be real-valued and cylindrically symmetric when V(x) is cylindrically symmetric and m is sufficiently large. This is a joint work with Lu Lu and Yong Luo.

报告人简介：李帅，华中农业大学副教授，2018年毕业于中科院武汉物理与数学研究所，师从郭玉劲教授。主要从事非线性泛函分析与偏微分方程的研究，主要研究成果发表于JFA、Trans.AMS、Nonlinearity、ZAMP等国际期刊。

报告题目2：Ground states of rotating two-component focusing bosegases

报告人：高永帅讲师，武汉工程大学

报告时间：2025年11月21日（周五）15:50-17:50

报告地点：#腾讯会议：894-541-502

报告摘要：In this talk, we are concerned with ground states of two-component Bose gases confined in a harmonic trap V(x)=x₁²+∧²x₂² rotating at the velocity Ω>0, where ∧≥1 and (x₁, x₂)∈R². We focus on the case where the intraspecies interaction (-a₁, -a₂) and the interspecies interaction -β are both attractive, i.e, a₁, a₂ and β are all positive. It is shown that for any 0<Ω<Ω^*:=2, ground states exist if and only if 0<a₁, a₂<a^*:=||w||₂² and 0<β<β^*:=a^*+√[(a^*- a₁)( a^*- a₂)], where w>0 is the unique positive solution of -Δw+w-w³=0 in R². By deriving the refined expansions, we further prove the nonexistence of vortices for ground states as β↗β^*, where 0<Ω<Ω^* and 0<a₁, a₂<a^* are fixed.

报告人简介：高永帅，武汉工程大学，讲师，2024年博士毕业于华中师范大学，师从郭玉劲教授。长期从事非线性偏微分方程、非线性泛函分析的研究，主要研究成果发表于Calc. Var. Partial Differ. Equ.、J. Differ. Equ.、J. Math. Anal. Appl.、Nonlinear Analysis等国际期刊。

邀请人：非线性分析与PDE团队