Analysis & PDE

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

Standing ring blowup solutions for cubic nonlinear Schrödinger equations

Ian Zwiers

Full-text: Open access

Abstract

For all dimensions N3 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
Received: 5 February 2010
Revised: 27 September 2010
Accepted: 14 November 2010
First available in Project Euclid: 20 December 2017

Permanent link to this document
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

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions

Keywords
focusing nonlinear Schrödinger equation supercritical collapse blowup rate blowup set codimension regularity log-log rate

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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