Speaker: 李步扬教授，香港理工大学

Inviter: 流体力学方程研究中心

Title: Computing rough solutions of the KdV equation below L2

Language: Chinese

Time & Venue: 2025.07.17 10:30-11:30 南楼N204

Abstract: We establish a novel framework for computing the solutions of the KdV equation in the negative Sobolev spaces with rigorous error analysis, where classical numerical methods fail due to their reliance on high regularity and instability at low regularity. The numerical analysisis established by combining a continuous reformulation of the numerical scheme, the Bourgain-space estimates for the continuous reformulation, and a rescaling strategy that reduces the reformulated problem to a small initial value, which allow us to bridge a critical gap between numerical analysis and theoretical well-posedness by designing a numerical method, through rigorous error analysis, for solving the KdV equation in the negative Sobolev spaces. The numerical scheme is proved to have nearly optimal-order convergence with respect to the spatial degrees of freedom in H-1/2 for initial data in Hs with s>-1/2.