JournalsrmiVol. 31, No. 2pp. 657–680

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

  • Farah Abou Shakra

    Dublin, Ireland
On 2D nonlinear Schrödinger equation on non-trapping exterior domains cover
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Abstract

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.

Cite this article

Farah Abou Shakra, On 2D nonlinear Schrödinger equation on non-trapping exterior domains. Rev. Mat. Iberoam. 31 (2015), no. 2, pp. 657–680

DOI 10.4171/RMI/849