Analysis & PDE

• Anal. PDE
• Volume 4, Number 5 (2011), 677-727.

Standing ring blowup solutions for cubic nonlinear Schrödinger equations

Ian Zwiers

Abstract

For all dimensions $N≥3$ we prove there exist solutions to the focusing cubic nonlinear Schrödinger equations that blow up on a set of codimension two. The blowup set is identified both as the site of $L2$ concentration and by a bounded supercritical norm outside any neighborhood of the set. In all cases, the global $H1$ norm grows at the log-log rate.

Article information

Source
Anal. PDE, Volume 4, Number 5 (2011), 677-727.

Dates
Revised: 27 September 2010
Accepted: 14 November 2010
First available in Project Euclid: 20 December 2017

https://projecteuclid.org/euclid.apde/1513731181

Digital Object Identifier
doi:10.2140/apde.2011.4.677

Mathematical Reviews number (MathSciNet)
MR2901563

Zentralblatt MATH identifier
1264.35241

Citation

Zwiers, Ian. Standing ring blowup solutions for cubic nonlinear Schrödinger equations. Anal. PDE 4 (2011), no. 5, 677--727. doi:10.2140/apde.2011.4.677. https://projecteuclid.org/euclid.apde/1513731181

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