Two dimensional water waves in holomorphic coordinates II: global solutions

TL;DR

This paper proves that small localized initial data for the two-dimensional infinite depth water wave equation in holomorphic coordinates results in global solutions, extending previous work by the authors.

Contribution

It introduces a new approach to establish global existence for 2D water waves using holomorphic coordinates, building on prior research.

Findings

Small localized data leads to global solutions

Holomorphic coordinates effectively analyze water wave equations

Extension of previous results to broader initial conditions

Abstract

This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates,and prove that small localized data leads to global solutions. This article is a continuation of authors' earlier paper arXiv:1401.1252.