Hadamard well-posedness of the gravity water waves system

被引:2
作者
Quang-Huy Nguyen [1 ]
机构
[1] Univ Paris Sud, Dept Math Orsay, F-91405 Orsay, France
关键词
Gravity water wave; Hadamard well-posedness; flow map; FREE-SURFACE; SOBOLEV SPACES; EQUATIONS; MOTION;
D O I
10.1142/S0219891616500211
中图分类号
O29 [应用数学];
学科分类号
070104 ;
摘要
We consider the system of (pure) gravity water waves in any dimension and in a fluid domain with a general bottom geometry. The unique solvability of this problem was established by Alazard-Burq-Zuily [Invent. Math. 198(1) (2014) 71-163] at a low regularity level where the initial surface is C3/2 + in terms of Sobolev embeddings; this result allows the existence of free surfaces with unbounded curvature. Our result states that the solutions obtained in the above work depend continuously on initial data in the strong topology in which the solutions are constructed. This establishes a well-posedness result in the sense of Hadamard.
引用
收藏
页码:791 / 820
页数:30
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