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GLOBAL WELL-POSEDNESS AND INSTABILITY OF A NONLINEAR SCHRÖDINGER EQUATION WITH HARMONIC POTENTIAL

Part of: Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  14 October 2014

T. SAANOUNI
T. SAANOUNI*
Affiliation:
University of Tunis El Manar, Faculty of Sciences of Tunis, LR03ES04 Partial Differential Equations and Applications, 2092 Tunis, Tunisia email tarek.saanouni@ipeiem.rnu.tn
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Abstract

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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.

Keywords

nonlinear Schrödinger equationpotentialwell-posednessblow-upMoser–Trudinger inequalityground state

MSC classification

Primary: 35Q55: NLS-like equations (nonlinear Schrödinger)
Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 98 , Issue 1 , February 2015 , pp. 78 - 103
Copyright
Copyright © 2014 Australian Mathematical Publishing Association Inc. 

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