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1 February 2014 On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation
Frank Merle, Pierre Raphaël, Jeremie Szeftel
Duke Math. J. 163(2): 369-431 (1 February 2014). DOI: 10.1215/00127094-2430477

Abstract

We consider the nonlinear Schrödinger equation itu+Δu+u|u|p1=0 in dimension N2 and in the mass supercritical and energy subcritical range 1+4N<p<min {N+2N2,5}. For initial data u0H1 with radial symmetry, we prove a universal upper bound on the blow-up speed. We then prove that this bound is sharp and attained on a family of collapsing ring blow-up solutions first formally predicted in Fibich et al.

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Frank Merle. Pierre Raphaël. Jeremie Szeftel. "On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation." Duke Math. J. 163 (2) 369 - 431, 1 February 2014. https://doi.org/10.1215/00127094-2430477

Information

Published: 1 February 2014
First available in Project Euclid: 29 January 2014

zbMATH: 1292.35283
MathSciNet: MR3161317
Digital Object Identifier: 10.1215/00127094-2430477

Subjects:
Primary: 35Q55
Secondary: 35Q51

Rights: Copyright © 2014 Duke University Press

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Vol.163 • No. 2 • 1 February 2014
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