关于举行数学学院2026年海外优青分论坛的通知

报告主题: Local-in-Time Existence of $L^1$ Solutions to the Gravity Water Wave Kinetic Equation

报 告 人: 吴晓旭博士 澳大利亚国立大学

报告时间： 2026年5月15日（星期五） 上午10:30-11:30

报告地点： 37号楼3A01报告厅

欢迎广大师生前往！

数学学院

2026年5月12日

报告摘要：

The gravity water wave kinetic equation, written down by Hasselmann in 1962, underlies modern ocean wave forecasting and climate modelling and was central to Hasselmann's 2021 Nobel Prize. Yet the basic mathematical question — does it admit solutions? — has remained open for 64 years, owing to a collision kernel that is widely considered the most singular in physical kinetic theory.

In this talk I will present joint work with Yulin Pan establishing the first local-in-time existence of strong $L^1$ solutions in dimensions $d \ge 2$, for nonnegative initial data in a weighted $L^2 \cap L^\infty$ space. The proof rests on (i) a new kernel estimate that rigorously confirms the Zakharov–Geogjaev asymptotics — at most quadratic growth in the large wavenumber — and (ii) a decomposition of the linearised collision operator into a dissipative part plus a bounded perturbation, preserved under polynomial weights. Quadratic kernel growth turns out to be exactly the threshold at which this decomposition closes. The result also supplies an analytic ingredient needed for the full derivation programme connecting the free-surface Euler equations to the wave kinetic description.

报告人介绍：

吴晓旭博士2017年本科毕业于华中师范大学数学科学学院，2023年5月博士毕业于罗格斯大学，师从Avy Soffer 教授。2023年8月-2024年5月Texas A&M University访问助理教授，2024年1月-2024年6月The Fields Institute, Toronto 博士后， 2024年8月至今在澳大利亚国立大学进行博士后研究工作。其研究方向涉及PDE,  Scattering Theory, Quantum field theory, Quantum information, Quantum algorithms,Kinetic Theory and application in ocean engineering等。相关成果发表在ARMA, Adv. Math., CMP, TAMS, LMP等知名数学期刊。