Global Regularity for 2 D Water Waves with Surface Tension

@inproceedings{Ionescu2014GlobalRF,
title={Global Regularity for 2 D Water Waves with Surface Tension},
author={A D Ionescu and Fabio Giuseppe Pusateri},
year={2014}
}

We consider the full irrotational water waves system with surface tension and no gravity in dimension two (the capillary waves system), and prove global regularity and modified scattering for suitably small and localized perturbations of a flat interface. An important point of our analysis is to develop a sufficiently robust method (the “quasilinear I-method”) which allows us to deal with strong singularities arising from time resonances in the applications of the normal form method (the so… CONTINUE READING