Standard time-stepping techniques require a regularity constraint on the initial data $u_0$ for dispersive equations. We introduce a class of low regularity integrators for problems where certain constraints are not satisfied. Moreover, when the regularity is critically low ($u_0\in H^s$ with $s\leq d/2$), the classical stability argument based on Sobolev spaces does not hold. We have developed a discrete Bourgain framework that overcomes this problem. In this talk, I will use several different dispersive models to summarize how these techniques are applied.

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。