Two dimensional water waves in holomorphic coordinates II: global solutions
نویسندگان
چکیده
منابع مشابه
Two Dimensional Water Waves in Holomorphic Coordinates Ii: Global Solutions
This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates, and prove that small localized data leads to global solutions. This article is a continuation of authors’ earlier paper [11].
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Abstract. This article is concerned with the infinite depth water wave equation in two space dimensions. We consider this problem expressed in position-velocity potential holomorphic coordinates. Viewing this problem as a quasilinear dispersive equation, we establish two results: (i) local well-posedness in Sobolev spaces, and (ii) almost global solutions for small localized data. Neither of th...
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ژورنال
عنوان ژورنال: Bulletin de la Société mathématique de France
سال: 2016
ISSN: 0037-9484,2102-622X
DOI: 10.24033/bsmf.2717