中国科学院数学与系统科学研究院
数学研究所
数学科学全国重点实验室
偏微分方程讨论班
Speaker: 单敏捷（中央民族大学）
Inviter: 范晨捷
Language: Chinese
Title: Well-Posedness of KdV in H⁻¹(ℝ): Regular Commuting Flows and Vanishing Residual Dynamics
Time & Venue: 2026年9月17日（星期四） 15:00-16:30 思源楼S803
Abstract: This talk presents the main dynamical mechanism in Killip and Vişan's proof of well-posedness for the KdV equation in H⁻¹. Using spectral invariants, we construct regular Hamiltonian flows H_κ that commute exactly with the KdV flow, allowing the original dynamics to be factored into a regular flow and a residual flow. By working in coordinates defined through the diagonal Green's function and combining equicontinuity with a reconstruction cancellation, we show that the residual flow converges uniformly to the identity on bounded time intervals. This provides the key step toward constructing a continuous KdV flow in H⁻¹.
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