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

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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.

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Authors and Affiliations

  1. LR03ES04 Partial Differential Equations and Applications, Faculty of Science of Tunis, University of Tunis El Manar, 2092, Tunis, Tunisia

    T. Saanouni

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  1. T. Saanouni
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Correspondence to T. Saanouni.

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T. Saanouni is grateful to the Laboratory of PDE and Applications at the Faculty of Sciences of Tunis.

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Saanouni, T. Global Well-Posedness and Instability of an Inhomogeneous Nonlinear Schrödinger Equation. Mediterr. J. Math. 12, 387–417 (2015). https://doi.org/10.1007/s00009-014-0403-4

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  • DOI: https://doi.org/10.1007/s00009-014-0403-4

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