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GLOBAL WELL-POSEDNESS AND INSTABILITY OF A NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL
Published online by Cambridge University Press: 14 October 2014
Abstract
This paper is concerned with the Cauchy problem for a nonlinear Schrödinger equation with a harmonic potential and exponential growth nonlinearity in two space dimensions. In the defocusing case, global well-posedness is obtained. In the focusing case, existence of nonglobal solutions is discussed via potential-well arguments.
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- Copyright © 2014 Australian Mathematical Publishing Association Inc.