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arXiv · 2511.06629

Stability of Solitary Capillary-Gravity Water Waves in Three Dimensions

Changfeng Gui·Shanfa Lai·Yong Liu·Juncheng Wei·Wen Yang
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Abstract

This paper establishes the conditional orbital stability of fully localized solitary waves for the three-dimensional capillary-gravity water wave problem in finite depth under strong surface tension. The waves, constructed via a non-variational Lyapunov-Schmidt reduction in [26], are not energy minimizers and thus require a direct stability analysis. We adapt the Grillakis-Shatah-Strauss framework within Mielke's approach to handle the mismatch between well-posedness and energy spaces. The proof relies on spectral analysis of the linearized dynamics and careful treatment of the Hamiltonian structure defined by the energy and momentum functionals.

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Changfeng Gui, Shanfa Lai, Yong Liu, Juncheng Wei, Wen Yang. 2025-11-10. Stability of Solitary Capillary-Gravity Water Waves in Three Dimensions. https://arxiv.org/abs/2511.06629

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