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Mediterranean Journal of Mathematics

, Volume 12, Issue 2, pp 387–417 | Cite as

Global Well-Posedness and Instability of an Inhomogeneous Nonlinear Schrödinger Equation

  • T. Saanouni
Article
  • 130 Downloads

Abstract

This paper is concerned with the Cauchy problem for an inhomogeneous nonlinear Schrödinger equation with exponential growth nonlinearity in two space dimensions. We prove global well-posedness, existence of the associated ground state and instability by blow-up.

Mathematics Subject Classification (2000)

35Q55 

Keywords

Nonlinear Schrödinger equation well-posedness blow-up Moser–Trudinger inequality 

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Copyright information

© Springer Basel 2014

Authors and Affiliations

  1. 1.LR03ES04 Partial Differential Equations and Applications, Faculty of Science of TunisUniversity of Tunis El ManarTunisTunisia

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