Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4610535 | Journal of Differential Equations | 2013 | 91 Pages |
Abstract
We prove the existence of a minimiser of E subject to the constraint I=2μ, where 0<μâª1. The existence of a small-amplitude solitary wave is thus assured, and since E and I are both conserved quantities a standard argument may be used to establish the stability of the set Dμ of minimisers as a whole. 'Stability' is however understood in a qualified sense due to the lack of a global well-posedness theory for three-dimensional water waves. We show that solutions to the evolutionary problem starting near Dμ remain close to Dμ in a suitably defined energy space over their interval of existence; they may however explode in finite time due to higher-order derivatives becoming unbounded.
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
B. Buffoni, M.D. Groves, S.M. Sun, E. Wahlén,