Sharp weights in the Cauchy problem for nonlinear Schrödinger equations with potential

被引：0
作者：
Rémi Carles
机构：
[1] CNRS & Univ. Montpellier,
来源：
Zeitschrift für angewandte Mathematik und Physik | 2015年 / 66卷
关键词：
Nonlinear Schrodinger equation; Unbounded potential; Cauchy problem; 35Q55; 35A05;
D O I：
暂无
中图分类号：
学科分类号：
摘要：
We review different properties related to the Cauchy problem for the (nonlinear) Schrödinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.
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页码：2087 / 2094
页数：7
相关论文
共 29 条
[1]  
Ben Abdallah N.(2008)Time averaging for the strongly confined nonlinear Schrödinger equation, using almost periodicity J. Differ. Equ. 245 154-200
[2]  
Castella F.(1993)Fourier transform restriction phenomena for certain lattice subsets and applications to nonlinear evolution equations. I. Schrödinger equations Geom. Funct. Anal. 3 107-156
[3]  
Méhats F.(2004)Strichartz inequalities and the nonlinear Schrödinger equation on compact manifolds Am. J. Math. 126 569-605
[4]  
Bourgain J.(2007)WKB analysis for nonlinear Schrödinger equations with potential Commun. Math. Phys. 269 195-221
[5]  
Burq N.(2008)On the Cauchy problem in Sobolev spaces for nonlinear Schrödinger equations with potential Portugal. Math. (N. S.) 65 191-209
[6]  
Gérard P.(2011)Nonlinear Schrödinger equation with time dependent potential Commun. Math. Sci. 9 937-964
[7]  
Tzvetkov N.(1990)The Cauchy problem for the critical nonlinear Schrödinger equation in Nonlinear Anal. TMA 14 807-836
[8]  
Carles R.(2009)Smoothing estimates for the Schrödinger equation with unbounded potentials J. Differ. Equ. 246 4552-4567
[9]  
Carles R.(1979)A construction of the fundamental solution for the Schrödinger equation J. Analyse Math. 35 41-96
[10]  
Carles R.(1979)On a class of nonlinear Schrödinger equations. I The Cauchy problem, general case J. Funct. Anal. 32 1-32
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