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

Speaker: 赖善发 博士 澳门大学

Inviter:  秦国林

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

Language: Chinese

Time & Venue: 2025.12.25 16:00-17:00  南楼933

Abstract: 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.