Small data blow-up of L 2 or H 1-solution for the semilinear Schrodinger equation without gauge invariance

被引：34
作者：
Ikeda, Masahiro [1 ]
Inui, Takahisa [1 ]
机构：
[1] Kyoto Univ, Grad Sch Sci, Dept Math, Kyoto, Kyoto 6068502, Japan
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2015年 / 15卷 / 03期
关键词：
Critical exponent; Nonlinear Schrodinger equation; Nongauge invariance; L-2-subcritical; Strauss exponent; CAUCHY-PROBLEM; CRITICAL EXPONENTS; EXISTENCE;
D O I：
10.1007/s00028-015-0273-7
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the initial value problem for the semilinear Schrodinger equation: i partial derivative(t)u + Delta u = lambda vertical bar u vertical bar(p,) (t, d) is an element of [0, T)x R-n, (NLS) where p > 1, lambda is an element of C\. {0}. In this paper, we will prove a small data blow-up result of L-2 and H-1-solution for (NLS) in 1 < p < 1 + 4/n. Also, an upper bound of the life span will be given (Theorem 2.2).
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页码：571 / 581
页数：11
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