Capillary-Gravity Water Waves: Modified Flow Force Formulation
arXiv:2010.09521 · doi:10.1016/j.jde.2020.08.012
Abstract
The classical irrotational capillary-gravity water wave problem described by the Euler equations with a nonlinear free surface boundary condition over a flat bed is considered. A modified flow force has been defined and a new formulation of capillary-gravity waves in the framework of the modified flow force function has been developed. Using bifurcation theory, the local existence of waves of small amplitude is proved.