WELL-POSEDNESS AND SCATTERING FOR A SYSTEM OF QUADRATIC DERIVATIVE NONLINEAR SCHRODINGER EQUATIONS WITH LOW REGULARITY INITIAL DATA

被引：16

作者：

Hirayama, Hiroyuki ^{[1
]}

机构：

[1] Nagoya Univ, Grad Sch Math, Chikusa Ku, Nagoya, Aichi 4648602, Japan

来源：

COMMUNICATIONS ON PURE AND APPLIED ANALYSIS | 2014年 / 13卷 / 04期

关键词：

Schrodinger equation; well-posedness; Cauchy problem; scaling critical; Bilinear estimate; bounded p-variation; BENJAMIN-ONO-EQUATION; STANDING WAVES;

D O I：

10.3934/cpaa.2014.13.1563

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In the present paper, we consider the Cauchy problem of a system of quadratic derivative nonlinear Schrodinger equations which was introduced by M. Colin and T. Colin (2004) as a model of laser-plasma interaction. The local existence of the solution of the system in the Sobolev space H-s for s > d/2 + 3 is proved by M. Colin and T. Colin. We prove the well-posedness of the system with low regularity initial data. For some cases, we also prove the well-posedness and the scattering at the scaling critical regularity by using U-2 space and V-2 space which are applied to prove the well-posedness and the scattering for KP-II equation at the scaling critical regularity by Hadac, Herr and Koch (2009).

引用

页码：1563 / 1591

页数：29

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