报告人：纪伦

报告题目：Bourgain techniques for low regularity error estimates

时间：2025年9月15日 10:30-11:30

地点：数学楼2-3会议室

报告摘要：

The Zakharov system presents unique analytical and numerical challenges due to the presence of a Laplacian in the nonlinearity. This feature induces a mechanism of regularity loss, which in turn leads to numerical instabilities. Classical approaches circumvent this issue by reformulating the system; however, such reformulations compromise the intrinsic geometric structure, which is closely tied to the system’s conservation behavior. In this work, we introduce a new convergence result for numerical methods applied directly to the original Zakharov system. By employing discrete Bourgain techniques, we are able, for the first time, to overcome the obstacle of regularity loss without reformulations. Our analysis establishes convergence for initial data of extremely low regularity, while the resulting schemes additionally exhibit strikingly robust conservation behavior. In this talk, In this talk, I will review the key concepts of our approach and its implications for the numerical analysis of Zakharov system and other dispersive models in low regularity.

报告人简介：

纪伦，香港理工大学博士后。于2017年在中国科学技术大学取得学士学位，于2024年在奥地利因斯布鲁克大学、2025年在中国科学院数学与系统科学研究院分别取得博士学位。纪伦博士致力于色散类偏微分方程数值求解方法及分析方面的研究，主要关注则初值条件下的算法设计及误差估计，相关工作发表在SIAM J. Numer. Anal., Math. Comp.等计算数学权威期刊上。