Global well-posedness and blow-up on the energy space for the inhomogeneous nonlinear Schrodinger equation

被引：86
|
作者：
Farah, Luiz G. [1 ]
机构：
[1] Univ Fed Minas Gerais, ICEx, Av Antonio Carlos,6627,Caixa Postal 702, BR-30123970 Belo Horizonte, MG, Brazil
来源：
JOURNAL OF EVOLUTION EQUATIONS | 2016年 / 16卷 / 01期
关键词：
SCATTERING; UNIQUENESS; EXISTENCE;
D O I：
10.1007/s00028-015-0298-y
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
We consider the supercritical inhomogeneous nonlinear Schrodinger equation i partial derivative(t)u + Delta u + vertical bar x vertical bar(-b) vertical bar u vertical bar(2 sigma) u = 0, where and (2-b)/N < sigma < (2-b)/(N-2) and 0 < b < min{2, N}. We prove a Gagliardo-Nirenberg-type estimate and use it to establish sufficient conditions for global existence and blow-up in H-1 (R-N).
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页码：193 / 208
页数：16
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