Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 1, pp. 139-170.

In this paper we concentrate on the analysis of the critical mass blowing-up solutions for the cubic focusing Schrödinger 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 ${\left(T-t\right)}^{-1}$, the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

Classification: 35Q55,  35B33,  35B40,  35Q40
Banica, Valeria 1

1 Dipartimento di Matematica Università di Pisa Via F. Buonarroti 2 56127 Pisa, Italy
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Banica, Valeria. Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain. Annali della Scuola Normale Superiore di Pisa - Classe di Scienze, Serie 5, Volume 3 (2004) no. 1, pp. 139-170. http://archive.numdam.org/item/ASNSP_2004_5_3_1_139_0/

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