Scattering theory for radial nonlinear Schrodinger equations on hyperbolic space

被引：34

作者：

Banica, Valeria ^{[1
]}

Carles, Remi ^{[2
,3
]}

Staffilani, Gigliola ^{[4
]}

机构：

[1] Univ Evry, Dept Math, F-91025 Evry, France

[2] CNRS, F-34095 Montpellier 5, France

[3] Univ Montpellier 2, F-34095 Montpellier 5, France

[4] MIT, Cambridge, MA 02139 USA

来源：

GEOMETRIC AND FUNCTIONAL ANALYSIS | 2008年 / 18卷 / 02期

基金：

美国国家科学基金会;

关键词：

nonlinear Schrodinger equations on manifolds; asymptotic behavior; Strichartz estimates; Morawetz estimates;

D O I：

10.1007/s00039-008-0663-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

We study the long-time behavior of radial solutions to nonlinear Schrodinger equations on hyperbolic space. We show that the usual distinction between short-range and long-range nonlinearity is modified: the geometry of the hyperbolic space makes every power-like nonlinearity short range. The proofs rely on weighted Strichartz estimates, which imply Strichartz estimates for a broader family of admissible pairs, and on Morawetz-type inequalities. The latter are established without symmetry assumptions.

引用

页码：367 / 399

页数：33

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