走向现代数学学术报告 - 李帅副教授（No. 917)

报告题目：Uniqueness and cylindrical symmetry of ground states for magnetic nonlinear Choquard equation

报告时间：2026年4月12日 8:45

报告地点：东海岸校区-D实209

报 告 人：李帅 副教授（华中农业大学）

邀 请 人：王大斌、谢华飞

报告摘要：This talk focuses on ground states of the following magnetic nonlinear Choquard equation: $$ -\Delta_A u+V(x) u=\mu u+\left(I_2 *|u|^2\right) u \quad \text { in } R^3, $$ where $\boldsymbol{u} \in \boldsymbol{H}^{\mathbf{1}}\left(\boldsymbol{R}^{\mathbf{3}}, \boldsymbol{C}\right)$ satisfies $|\boldsymbol{u}|_{\mathbf{2}}^{\mathbf{2}}=\boldsymbol{m}>\mathbf{0}, \boldsymbol{V}(\boldsymbol{x}) \in \boldsymbol{L}^{\infty}\left(\boldsymbol{R}^{\mathbf{3}}\right), \boldsymbol{I}_{\mathbf{2}}:=\frac{\mathbf{1}}{\mathbf{4} \pi|\boldsymbol{x}|}$ is the Riesz potential and $\Delta_A$ denotes the magnetic Laplacian. By considering the associated constrained minimization problem $\boldsymbol{e}_{\boldsymbol{A}}(\boldsymbol{m})$, 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 $\boldsymbol{m} \rightarrow \infty$ by establishing the expansion of $\boldsymbol{e}_A(\boldsymbol{m})$ 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 $\boldsymbol{V}(\boldsymbol{x})$ is cylindrically symmetric and $\boldsymbol{m}$ 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年博士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。主持国家自然科学基金项目两项。主要研究成果发表于JFA、Trans. AMS.、Nonlinearity、ZAMP等国际期刊。