# MathSciDoc: An Archive for Mathematician ∫

#### Analysis of PDEsmathscidoc:1906.03002

Communications on pure and applied mathematics, 71, (1), 90-162, 2018
We prove global existence and a modified scattering property for the solutions of the 2D gravity water waves system in the infinite depth setting for a class of initial data, which is only required to be small above the level \dot{H}^{1/5}\times \dot{H}^{1/2+1/5}. No assumption is made below this level. Therefore, the nonlinear solution can have infinite energy. As a direct consequence, the momentum condition assumed on the physical velocity in all previous small energy results by Ionescu‐Pusateri, Alazard‐Delort, and Ifrim‐Tataru is removed.
gravity water waves, global regularity
@inproceedings{xuecheng2018global,
title={Global infinite energy solutions for the 2D gravity water waves system},
author={Xuecheng Wang},
url={http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190626140739961359368},
booktitle={Communications on pure and applied mathematics},
volume={71},
number={1},
pages={90-162},
year={2018},
}

Xuecheng Wang. Global infinite energy solutions for the 2D gravity water waves system. 2018. Vol. 71. In Communications on pure and applied mathematics. pp.90-162. http://archive.ymsc.tsinghua.edu.cn/pacm_paperurl/20190626140739961359368.