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, p. 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 (T-t) -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
@article{ASNSP_2004_5_3_1_139_0,
     author = {Banica, Valeria},
     title = {Remarks on the blow-up for the Schr\"odinger equation with critical mass on a plane domain},
     journal = {Annali della Scuola Normale Superiore di Pisa - Classe di Scienze},
     publisher = {Scuola Normale Superiore, Pisa},
     volume = {Ser. 5, 3},
     number = {1},
     year = {2004},
     pages = {139-170},
     zbl = {1170.35528},
     mrnumber = {2064970},
     language = {en},
     url = {http://www.numdam.org/item/ASNSP_2004_5_3_1_139_0}
}
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://www.numdam.org/item/ASNSP_2004_5_3_1_139_0/

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