Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
8898164 | Annales de l'Institut Henri Poincare (C) Non Linear Analysis | 2017 | 44 Pages |
Abstract
This article is devoted to the Cauchy problem for the 2D gravity-capillary water waves in fluid domains with general bottoms. Local well-posedness for this problem with Lipschitz initial velocity was established by Alazard-Burq-Zuily [1]. We prove that the Cauchy problem in Sobolev spaces is uniquely solvable for initial data 14-derivative less regular than the aforementioned threshold, which corresponds to the gain of Hölder regularity of the semi-classical Strichartz estimate for the fully nonlinear system. In order to obtain this Cauchy theory, we establish global, quantitative results for the paracomposition theory of Alinhac [5].
Keywords
Related Topics
Physical Sciences and Engineering
Mathematics
Analysis
Authors
Huy Quang Nguyen,