Local existence in time of solutions to the elliptic-hyperbolic Davey-Stewartson system without smallness condition on the data

被引：0
作者：
Nakao Hayashi
机构：
[1] Science University of Tokyo,Department of Applied Mathematics
来源：
Journal d’Analyse Mathématique | 1997年 / 73卷
关键词：
Global Existence; Smallness Condition; Local Existence; Small Solution; Weighted Sobolev Space;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We study the initial value problem for the elliptic-hyperbolic Davey-Stewartson systems {ie133-01} where {ie133-2},u is a complex valued function and φ is a real valued function. When (c1,c2) = (-1, 2) the system (*) is called DSI equation in the inverse scattering literature. Our purpose in this paper is to prove the local existence of a unique solution to (*) in the Sobolev spaceH2(R2) without the smallness condition on the data which were assumed in previous works [7], [17], [19], [26], Our result is a positive answer to Question 7 in [24].
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页码：133 / 164
页数：31
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