Global infinite energy solutions for the 2D gravity water waves system

Xuecheng Wang Tsinghua University

Analysis of PDEs mathscidoc: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
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@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.
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