A sharp Cauchy theory for the 2D gravity-capillary waves

  • Huy Quang Nguyen

    UMR 8628 du CNRS, Laboratoire de Mathématiques d'Orsay, Université Paris-Sud, 91405 Orsay Cedex, France


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 -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].

Cite this article

Huy Quang Nguyen, A sharp Cauchy theory for the 2D gravity-capillary waves. Ann. Inst. H. Poincaré Anal. Non Linéaire 34 (2017), no. 7, pp. 1793–1836

DOI 10.1016/J.ANIHPC.2016.12.007