中科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

偏微分方程研讨班

Speaker: 单敏捷（中央民族大学）

Inviter: 范晨捷

Language: Chinese

Title：Low regularity well-posedness for the completely integrable dispersive PDEs

Time&Venue：2025年9月19日(星期五) 10:00-11:00&思源楼S803

Abstract: We will introduce Killip-Visan’s new method of general applicability for the study of low-regularity well-posedness for integrable PDE. Starting from the Lax pair, the perturbation determinant, a series of conserved quantities, we will briefly recall the Hamiltonian commuting flow which provides a good approximation to the original Hamiltonian. The global well-posedness for the Hamiltonian evolution induced by the commuting flow is relatively easier to established in Sobolev spaces with low regularity. Then one can obtain the global well-posedness for the original dispersive equation from the global well-posedness for the approximate Hamiltonian evolution.