Displaying similar documents to “Remarks on global existence and compactness for L 2 solutions in the critical nonlinear schrödinger equation in 2D”

Blow up and near soliton dynamics for the L 2 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 u t + ( u x x + u 5 ) x = 0 for initial data in H 1 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 H 1 , construction of various exotic blow up rates in H 1 , including grow up in infinite time. ...

Two blow-up regimes for L 2 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 i ∂ t u + Δ u + u | u | p - 1 = 0 . 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.

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 ( T - t ) - 1 , the expected one. Moreover, we show that blow-up cannot occur on the boundary, under certain geometric conditions on the domain. ...