Mathematics – Analysis of PDEs
Scientific paper
2011-08-09
Mathematics
Analysis of PDEs
83 pages, 1 figure
Scientific paper
In this paper we show that the hydrodynamic problem for three-dimensional water waves with strong surface-tension effects admits a fully localised solitary wave which decays to the undisturbed state of the water in every horizontal direction. The proof is based upon the classical variational principle that a solitary wave of this type is a critical point of the energy subject to the constraint that the momentum is fixed. We prove the existence of a minimiser of the energy subject to the constraint that the momentum is fixed and small. The existence of a small-amplitude solitary wave is thus assured, and since the energy and momentum are both conserved quantities a standard argument may be used to establish the stability of the set 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.
Buffoni Boris
Groves Mark D.
Sun Shu-Ming
Wahlén Erik
No associations
LandOfFree
Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.
If you have personal experience with Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Existence and conditional energetic stability of three-dimensional fully localised solitary gravity-capillary water waves will most certainly appreciate the feedback.
Profile ID: LFWR-SCP-O-70073