勷勤数学•专家报告

题      目：Global Well-Posedness for the Modified Whitham Equations

报  告  人： 崔翰 博士  (邀请人：罗天文)

                                       香港中文大学

时      间： 10月15日  10:30-11:30

地     点：数学科学学院西楼114

报告人简介:

        崔翰博士毕业于香港中文大学，研究方向为偏微分方程。

摘      要：

        In this talk, I will present a recent joint work with Yuexun Wang and Zhouping Xin establishing global existence and modified scattering for solutions to the modified Whitham equations with small, smooth, localized initial data. This work employs the space-time resonance method—a framework developed in recent years with numerous significant applications to the long-time behavior of dispersive equations. The main difficulties arise from the slow decay and the non-homogeneity of the dispersion relation. We overcome these by introducing an interaction multiplier theorem and by estimating weighted norms in frequency space. Due to loss of derivatives, the energy estimates are carried out in frequency space; moreover, we exploit the absence of time resonances by extracting good terms via integration by parts in time before the energy estimates.

         欢迎老师、同学们参加、交流！