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

2004/01/13 by Valeria Banica
Mathematics · #math.AP

paper · pdf

published as Ann. Sc. Norm. Super. Pisa (5), Vol. III (2004), 139-170 · 26 pages

arxiv created 2004/01/13 · arxiv updated 2009/12/01

Abstract

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.

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