报告题目 (Title)：Relaxation dynamics of the continuum Kuramoto model with non-integrable kernels （三）
具有非可积核的连续的Kuramoto模型的松弛动力学（三）
报告人 (Speaker)：Valeriia Zhidkova（博士生）
报告时间 (Time)：2026年6月25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 the final lecture, we use the uniform estimates obtained for the doubly regularized system to pass to the limit and construct global weak solutions for the original continuum Kuramoto model with non-integrable kernels. The convergence argument relies on energy dissipation estimates together with compactness methods in fractional Sobolev spaces. We then investigate the long-time behavior of solutions and prove exponential relaxation of the phase function toward the initial phase average in the L^2-norm. This provides a rigorous description of synchronization dynamics for continuum Kuramoto ensembles with strongly singular interactions.
