Global Analysis of a Model for Capillary Water Waves in Two Dimensions

In this paper we prove a global regularity result for a quadratic quasilinear model associated to the water waves system with surface tension and no gravity in dimension 2 (the capillary waves system). The model we consider here retains most of the difficulties of the full capillary water waves system, including the delicate time resonance structure and modified scattering. It is slightly simpler, however, at the technical level, and our goal here is to present our method in this simplified situation. The analysis of the full system is presented in a preprint by the authors (2014).