Existence and Stability of Solitary Capillary-Gravity Water-Wave in Three Dimensions

：赖善发（澳门大学）
：2026-01-10 09:20
：海韵园实验楼S102

报告人：赖善发（澳门大学）

时  间：2026年1月10日9:20

地  点：海韵园实验楼S102

内容摘要:

This talk summarizes our work on travelling waves in the 3D gravity-capillary water wave problem. We first establish the existence of a fully localized solitary wave, analogous to a lump solution of the KP-I equation, in a specific parameter regime. Subsequently, we demonstrate the conditional orbital stability of these waves under strong surface tension. By adapting the GSS framework within Mielke's approach and employing spectral analysis, we prove their nonlinear stability despite their non-minimizing character. This presentation thus provides a complete story, from the construction of these unique 3D waves to a proof of their dynamic persistence.

个人简介：

赖善发，现于澳门大学从事博士后研究工作，合作导师为桂长峰教授。2024年于中国科学院数学与系统科学研究院获博士学位，师从曹道民研究员。主要研究方向为非线性分析与流体力学稳定性，聚焦于应用非线性分析方法研究流体动力学问题。相关成果发表在Math Ann, JFA, CVPDE, JDE, PAMS等重要学术期刊。

 

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