Wellposedness of the 2D full water wave equation in a regime that allows for non- $$C^1$$ C 1 interfaces
Wellposedness of the 2D full water wave equation in a regime that allows for non- $$C^1$$ C 1 interfaces
复制标题
二维全水波方程在允许非 $$C^1$$ C 1 界面的体系中的适定性
DOI：
10.1007/s00222-019-00867-4
复制
发表时间：
2019
影响因子：
3.1
通讯作者：
Wu, Sijue
中科院分区：
文献类型：
--
作者：
Wu, Sijue
我们在允许自由界面为非的状态下考虑二维重力水波方程。在这种制度下，只有简并的泰勒不等式成立，并且在奇点处简并。 Kinsey 和 Wu（Camb J Math 6(2):93–181, 2018）构建了能量泛函并证明了先验估计。能量泛函不仅对于索博列夫空间中的界面和速度是有限的，而且对于具有角峰的一类非界面也是有限的。在本文中，我们证明了对于任何给定的数据，在时间局部上，二维重力水波方程解的存在性、唯一性和稳定性。
We consider the two dimensional gravity water wave equation in a regime where the free interface is allowed to be non-. In this regime, only a degenerate Taylor inequalityholds, with degeneracy at the singularities. In Kinsey and Wu (Camb J Math 6(2):93–181, 2018) an energy functionalwas constructed and an a-priori estimate was proved. The energy functionalis not only finite for interfaces and velocities in Sobolev spaces, but also finite for a class of non-interfaces with angled crests. In this paper we prove the existence, uniqueness and stability of the solution of the 2d gravity water wave equation in the class where, locally in time, for any given data satisfying.