Two Dimensional Water Waves in Holomorphic Coordinates Ii: Global Solutions
نویسنده
چکیده
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].
منابع مشابه
Two Dimensional Water Waves in Holomorphic Coordinates
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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