Quadratic forms for the 1-D semilinear Schrodinger equation

被引：117
|
作者：
Kenig, CE
Ponce, G
Vega, L
机构：
[1] UNIV CALIF SANTA BARBARA, DEPT MATH, SANTA BARBARA, CA 93106 USA
[2] UNIV BASQUE COUNTRY, DEPT MATEMAT, E-48080 BILBAO, SPAIN
来源：
TRANSACTIONS OF THE AMERICAN MATHEMATICAL SOCIETY | 1996年 / 348卷 / 08期
关键词：
Schrodinger equation; bilinear estimates; well-posedness;
D O I：
10.1090/S0002-9947-96-01645-5
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
This paper is concerned with 1-D quadratic semilinear Schrodinger equations. We study local well posedness in classical Sobolev space H-s of the associated initial value problem and periodic boundary value problem. Our main interest is to obtain the lowest value of s which guarantees the desired local well posedness result. We prove that at least for the quadratic cases these values are negative and depend on the structure of the nonlinearity considered.
引用
收藏
页码：3323 / 3353
页数：31
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