Duke Mathematical Journal

On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation

Frank Merle, Pierre Raphaël, and Jeremie Szeftel

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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.

Article information

Source
Duke Math. J., Volume 163, Number 2 (2014), 369-431.

Dates
First available in Project Euclid: 29 January 2014

Permanent link to this document
https://projecteuclid.org/euclid.dmj/1391007590

Digital Object Identifier
doi:10.1215/00127094-2430477

Mathematical Reviews number (MathSciNet)
MR3161317

Zentralblatt MATH identifier
1292.35283

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35Q51: Soliton-like equations [See also 37K40]

Citation

Merle, Frank; Raphaël, Pierre; Szeftel, Jeremie. On collapsing ring blow-up solutions to the mass supercritical nonlinear Schrödinger equation. Duke Math. J. 163 (2014), no. 2, 369--431. doi:10.1215/00127094-2430477. https://projecteuclid.org/euclid.dmj/1391007590


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