Year: 2025
Type: preprint
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.
Source: arXiv (Cornell University)
Authors: Gui, Changfeng, Lai, Shanfa, Liu, Yong, Wei, Juncheng, Yang, Wen
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7104974832
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