Recent progress on the blow-up problem of Zakharov equations
Frank Merle (1995)
Journées équations aux dérivées partielles
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Displaying similar documents to “Remarks on global existence and compactness for solutions in the critical nonlinear schrödinger equation in 2D”
Recent progress on the blow-up problem of Zakharov equations
Blow up and near soliton dynamics for the critical gKdV equation
Yvan Martel, Frank Merle, Pierre Raphaël (2011-2012)
Séminaire Laurent Schwartz — EDP et applications
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These notes present the main results of [, , ] concerning the mass critical (gKdV) equation for initial data in close to the soliton. These works revisit the blow up phenomenon close to the family of solitons in several directions: definition of the stable blow up and classification of all possible behaviors in a suitable functional setting, description of the minimal mass blow up in , construction of various exotic blow up rates in , including grow up in infinite time. ...
Two blow-up regimes for supercritical nonlinear Schrödinger equations
Frank Merle, Pierre Raphaël, Jérémie Szeftel (2009-2010)
Séminaire Équations aux dérivées partielles
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We consider the focusing nonlinear Schrödinger equations . We prove the existence of two finite time blow up dynamics in the supercritical case and provide for each a qualitative description of the singularity formation near the blow up time.
On the blowup theory for the critical nonlinear Schrödinger equations
Sahbi Keraani (2004-2005)
Séminaire Équations aux dérivées partielles
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Construction of blowup solutions for the nonlinear Schrödinger equation with critical nonlinearity
Jean Bourgain, W. Wang (1997)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain
Valeria Banica (2004)
Annali della Scuola Normale Superiore di Pisa - Classe di Scienze
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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 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain. ...