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Blow up of solutions to the nonlinear Schroedinger equations on manifolds

Journal Article · · Journal of Mathematical Physics
DOI:https://doi.org/10.1063/1.2722560· OSTI ID:20929727
;  [1]
  1. Department of Mathematical Sciences, Tsinghua University, Peking 100084 (China)
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.
OSTI ID:
20929727
Journal Information:
Journal of Mathematical Physics, Journal Name: Journal of Mathematical Physics Journal Issue: 5 Vol. 48; ISSN JMAPAQ; ISSN 0022-2488
Country of Publication:
United States
Language:
English

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