A New Structure for the 2D water wave equation: Energy stability and Global well-posedness
数学专题报告
报告题目(Title)：A New Structure for the 2D water wave equation: Energy stability and Global well-posedness
报告人(Speaker)：苏庆堂 （中国科学院数学与系统科学研究院）
地点(Place)：后主楼1124
时间(Time)：2025年4月8日10：30-11：30
邀请人(Inviter)：袁迪凡
报告摘要
We study the two-dimensional gravity water waves with a one-dimensional interface with small initial data. Our main contributions include the development of two novel localization lemmas and a Transition-of-Derivatives method, which enable us to reformulate the water wave system into the following simplified structure:
$$(D_t^2-iA\partial_{\alpha})\theta=i\frac{t}{\alpha}|D_t^2\zeta|^2D_t\theta+R$$
where $R$ behaves well in the energy estimate. As a key consequence, we derive the uniform bound
\begin{equation}\label{abstract:uniform}
\sup_{t\geq 0}\Big(\norm{D_t\zeta(\cdot,t)}_{H^{s+1/2}}+\norm{\zeta_{\alpha}(\cdot,t)-1}_{H^s}\Big)\leq C\epsilon,
\end{equation}
which enhances existing global uniform energy estimates for 2D water waves by imposing less restrictive constraints on the low-frequency components of the initial data.
This is joint work with Siwei Wang (AMSS).
主讲人简介
苏庆堂，中国科学院数学与系统科学研究院晨兴数学中心副研究员，研究方向为水波方程的严格数学分析，在水波方程的长时间适定性、稳定性与不稳定性等问题取得了一系列成果，部分论文发表在Ann PDE、CMP、ARMA等国际著名刊物。
