Gravity Solitary Waves By Minimization: An Uncountable Family
We improve and simplify the minimization method for solitary waves in two cases: firstly, when the surface tension is weak (that is, the Bond number is < 1/3) and the depth is finite, and secondly, when the depth is infinite. In a previous work on the first case, minimizers were shown to exist for a sequence tending to 0 of values of the horizontal impulse. The main difficulty is that strict subadditivity in the concentration-compactness method is unsettled. Here we observe in both examples that strict subadditivity nevertheless holds for a set of horizontal impulses of positive measure and the related propagation speeds are estimated from above.
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Keywords: Capillary-gravity water waves ; solitary waves ; stability ; variational methods ; Concentration-Compactness Principle ; Conditional Energetic Stability ; Water-Waves ; Existence ; Mechanics ; Calculus ; Topology
Record created on 2010-11-30, modified on 2016-08-09