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15 August 2006 Existence and stability of a solution blowing up on a sphere for an L2-supercritical nonlinear Schrödinger equation
Pierre Raphaël
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Duke Math. J. 134(2): 199-258 (15 August 2006). DOI: 10.1215/S0012-7094-06-13421-X

Abstract

We consider the quintic two-dimensional focusing nonlinear Schrödinger equation iut=Δu|u|4u which is L2-supercritical. Even though the existence of finite-time blow-up solutions in the energy space H1 is known, very little is understood concerning the singularity formation. Numerics suggest the existence of a stable blow-up dynamic corresponding to a self-similar blowup at one point in space. We prove the existence of a different type of dynamic and exhibit an open set among the H1-radial distributions of initial data for which the corresponding solution blows up in finite time on a sphere. This is the first result of an explicit description of a blow-up dynamic in the L2-supercritical setting

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Pierre Raphaël. "Existence and stability of a solution blowing up on a sphere for an L2-supercritical nonlinear Schrödinger equation." Duke Math. J. 134 (2) 199 - 258, 15 August 2006. https://doi.org/10.1215/S0012-7094-06-13421-X

Information

Published: 15 August 2006
First available in Project Euclid: 8 August 2006

zbMATH: 1117.35077
MathSciNet: MR2248831
Digital Object Identifier: 10.1215/S0012-7094-06-13421-X

Subjects:
Primary: 35Q55
Secondary: 35B05 , 35Q51

Rights: Copyright © 2006 Duke University Press

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Vol.134 • No. 2 • 15 August 2006
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