Advances in Nonlinear Analysis (Aug 2019)
Sharp conditions of global existence for nonlinear Schrödinger equation with a harmonic potential
Abstract
The Cauchy problem of nonlinear Schrödinger 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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