Global Infinite Energy Solutions for the 2D Gravity Water Waves System
Global Infinite Energy Solutions for the 2D Gravity Water Waves System
复制标题
二维重力水波系统的全球无限能量解决方案
DOI：
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发表时间：
2015
期刊：
影响因子：
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通讯作者：
Xuecheng Wang
中科院分区：
文献类型：
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作者：
Xuecheng Wang
对于一类只需H·1/5×H·1/5+1/2以上的小的初值，证明了二维重力水波系统解的整体存在性和一个修正的散射性.在这一水平以下不作任何假设。因此，非线性解可以有无限的能量。其直接结果是，取消了Ionescu-Pusateri、Alazard-Delort和Ifrem-Tataru在之前所有小能量结果中对物理速度假设的动量条件。
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 H˙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.