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Title: Blow up of solutions to the nonlinear Schroedinger equations on manifolds

Abstract

In this paper, we partially settle down the long-standing open problem of the finite time blow-up property about the nonlinear Schroedinger equations on some Riemannian manifolds such as the standard 2-sphere S{sup 2} and the hyperbolic 2-space H{sup 2}(-1). Using the similar idea, we establish such blow-up results on higher dimensional standard sphere and hyperbolic n-space. Extensions to n-dimensional Riemannian warped product manifolds with n{>=}2 are also given.

Authors:
;  [1]
  1. Department of Mathematical Sciences, Tsinghua University, Peking 100084 (China)
Publication Date:
OSTI Identifier:
20929727
Resource Type:
Journal Article
Resource Relation:
Journal Name: Journal of Mathematical Physics; Journal Volume: 48; Journal Issue: 5; Other Information: DOI: 10.1063/1.2722560; (c) 2007 American Institute of Physics; Country of input: International Atomic Energy Agency (IAEA)
Country of Publication:
United States
Language:
English
Subject:
71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; MATHEMATICAL MANIFOLDS; MATHEMATICAL SOLUTIONS; MATHEMATICAL SPACE; NONLINEAR PROBLEMS; SCHROEDINGER EQUATION; SPHERES

Citation Formats

Ma Li, and Zhao Lin. Blow up of solutions to the nonlinear Schroedinger equations on manifolds. United States: N. p., 2007. Web. doi:10.1063/1.2722560.
Ma Li, & Zhao Lin. Blow up of solutions to the nonlinear Schroedinger equations on manifolds. United States. doi:10.1063/1.2722560.
Ma Li, and Zhao Lin. Tue . "Blow up of solutions to the nonlinear Schroedinger equations on manifolds". United States. doi:10.1063/1.2722560.
@article{osti_20929727,
title = {Blow up of solutions to the nonlinear Schroedinger equations on manifolds},
author = {Ma Li and Zhao Lin},
abstractNote = {In this paper, we partially settle down the long-standing open problem of the finite time blow-up property about the nonlinear Schroedinger equations on some Riemannian manifolds such as the standard 2-sphere S{sup 2} and the hyperbolic 2-space H{sup 2}(-1). Using the similar idea, we establish such blow-up results on higher dimensional standard sphere and hyperbolic n-space. Extensions to n-dimensional Riemannian warped product manifolds with n{>=}2 are also given.},
doi = {10.1063/1.2722560},
journal = {Journal of Mathematical Physics},
number = 5,
volume = 48,
place = {United States},
year = {Tue May 15 00:00:00 EDT 2007},
month = {Tue May 15 00:00:00 EDT 2007}
}