论文标题
低规律性的二维重力波II：全局解决方案
Two dimensional gravity waves at low regularity II: Global solutions
论文作者
论文摘要
本文代表了一系列论文的第二部分，这些论文涉及两个空间维度的水浪方程的低规律性解决方案。我们这里的重点是针对小型和局部数据的全球解决方案。事实证明，这种解决方案在[15、7、10、12]早些时候存在。本文我们的目标是改善这些结果，并证明在最小的规律性和初始数据的衰减假设下，全球适应性良好。这里的一个关键要素由我们的第一篇论文平衡的立方估计来表示。另一个是非线性矢量字段sobolev的不等式，这是最后两个作者在本杰明·莫诺方程的上下文中首次提出的想法[14]。
This article represents the second installment of a series of papers concerned with low regularity solutions for the water wave equations in two space dimensions. Our focus here is on global solutions for small and localized data. Such solutions have been proved to exist earlier in [15, 7, 10, 12] in much higher regularity. Our goal in this paper is to improve these results and prove global well-posedness under minimal regularity and decay assumptions for the initial data. One key ingredient here is represented by the balanced cubic estimates in our first paper. Another is the nonlinear vector field Sobolev inequalities, an idea first introduced by the last two authors in the context of the Benjamin-Ono equations [14].
