no. 7
A sharp Cauchy theory for the 2D gravity-capillary waves
Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1793-1836.

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].

DOI : 10.1016/j.anihpc.2016.12.007
Mots clés : Water waves, Cauchy problem, Semi-classical Strichartz estimate, Paracomposition 
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Nguyen, Huy Quang. A sharp Cauchy theory for the 2D gravity-capillary waves. Annales de l'I.H.P. Analyse non linéaire, Tome 34 (2017) no. 7, pp. 1793-1836. doi : 10.1016/j.anihpc.2016.12.007. http://www.numdam.org/articles/10.1016/j.anihpc.2016.12.007/

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