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Global Infinite Energy Solutions for the 2D Gravity Water Waves System
Author(s) -
Wang Xuecheng
Publication year - 2018
Publication title -
communications on pure and applied mathematics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 3.12
H-Index - 115
eISSN - 1097-0312
pISSN - 0010-3640
DOI - 10.1002/cpa.21711
Subject(s) - mathematics , energy (signal processing) , nonlinear system , momentum (technical analysis) , class (philosophy) , gravitational wave , property (philosophy) , mathematical analysis , gravity wave , energy–momentum relation , classical mechanics , physics , computer science , quantum mechanics , philosophy , statistics , finance , epistemology , artificial intelligence , economics
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 levelH ˙ 1 / 5 × H ˙ 1 / 5 + 1 / 2. 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.© 2017 Wiley Periodicals, Inc.