Revista Matemática Iberoamericana


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Volume 31, Issue 2, 2015, pp. 657–680
DOI: 10.4171/RMI/849

Published online: 2015-07-16

On 2D nonlinear Schrödinger equation on non-trapping exterior domains

Farah Abou Shakra

Global existence and scattering for the nonlinear defocusing Schrödinger equation in 2 dimensions are known for domains exterior to star-shaped obstacles and for nonlinearities that grow at least as the quintic power. In this paper, we extend the global existence result for all non-trapping obstacles and for nonlinearities with power strictly greater than quartic. For such nonlinearities, we also prove scattering for a class of so-called almost star-shaped obstacles.

Keywords: Schrödinger equation, scattering, almost star-shaped

Abou Shakra Farah: On 2D nonlinear Schrödinger equation on non-trapping exterior domains. Rev. Mat. Iberoamericana 31 (2015), 657-680. doi: 10.4171/RMI/849