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

Valeria Banica

Displaying similar documents to “Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain”

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

Valeria Banica (2003)

Journées équations aux dérivées partielles

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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 from below the blow-up rate 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 state that blow-up cannot occur on the boundary, under certain geometric conditions on the domain.

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 $i \partial_{t} u + Δ u + u {| u |}^{p - 1} = 0$ . 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.

Recent progress on the blow-up problem of Zakharov equations

Frank Merle (1995)

Journées équations aux dérivées partielles

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Blow-up for the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential

Jing Lu (2013)

Applicationes Mathematicae

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We give a sufficient condition under which the solutions of the energy-critical nonlinear wave equation and Schrödinger equation with inverse-square potential blow up. The method is a modified variational approach, in the spirit of the work by Ibrahim et al. [Anal. PDE 4 (2011), 405-460].

Blow-up of a nonlocal p-Laplacian evolution equation with critical initial energy

Yang Liu, Pengju Lv, Chaojiu Da (2016)

Annales Polonici Mathematici

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This paper is concerned with the initial boundary value problem for a nonlocal p-Laplacian evolution equation with critical initial energy. In the framework of the energy method, we construct an unstable set and establish its invariance. Finally, the finite time blow-up of solutions is derived by a combination of the unstable set and the concavity method.

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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Displaying similar documents to “Remarks on the blow-up for the Schrödinger equation with critical mass on a plane domain”