报告题目 (Title)：Relaxation dynamics of the continuum Kuramoto model with non-integrable kernels （一）
具有非可积核的连续的Kuramoto模型的松弛动力学（一）
报告人 (Speaker)： Valeriia Zhidkova（博士生）
报告时间 (Time)：2026年6月11日（周四）14:00
报告地点 (Place)：校本部GJ303
邀请人(Inviter)：王宇澄
主办部门：理学院数学系
报告摘要：In this series of talks, we study the continuum Kuramoto model with strongly singular interaction kernels of fractional Laplacian type. In this first lecture, we introduce the singular continuum Kuramoto equation, discuss its mathematical and physical motivation, and present the main analytical difficulties caused by the non-integrable interaction kernel. We then state the principal results concerning global weak solutions and exponential relaxation toward synchronization. Finally, we review the functional framework and the main analytical tools used throughout the series, including fractional Sobolev spaces, compactness methods, and the regularization procedure underlying the existence theory.
