4.6 Article

Sharp conditions of global existence for nonlinear Schrodinger equation with a harmonic potential

Journal

ADVANCES IN NONLINEAR ANALYSIS
Volume 9, Issue 1, Pages 882-894

Publisher

WALTER DE GRUYTER GMBH
DOI: 10.1515/anona-2020-0031

Keywords

nonlinear Schrodinger equation; harmonic potential; potential wells; global existence; invariant sets

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The Cauchy problem of nonlinear Schrodinger equation with a harmonic potential for describing the attractive Bose-Einstein condensate under the magnetic trap is considered. We give some sufficient conditions of global existence and finite time blow up of solutions by introducing a family of potential wells. Some different sharp conditions for global existence, and some invariant sets of solutions are also obtained here.

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