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

• Farah Abou Shakra ^[1]
  1. [1] Université Paris
• Localización: Revista matemática iberoamericana, ISSN 0213-2230, Vol. 31, Nº 2, 2015, págs. 657-680
• Idioma: inglés
• DOI: 10.4171/RMI/849
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• Resumen

  • 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.