Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain

• Valeria Banica ^[1]
  1. [1] University of Pisa

     University of Pisa

     Pisa, Italia

     
• Localización: Annali della Scuola Normale Superiore di Pisa. Classe di scienze, ISSN 0391-173X, Vol. 3, Nº 1, 2004, págs. 139-170
• Idioma: inglés
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• Resumen

  • In this paper we concentrate on the analysis of the critical mass blowingup solutions for the cubic focusing Schr¨odinger equation with Dirichlet boundary conditions, posed on a plane domain. We bound the blow-up rate from below, for bounded and unbounded domains. If the blow-up occurs on the boundary, the blow-up rate is proved to grow faster than (T −t) −1, the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.