Analysis & PDE
- Anal. PDE
- Volume 4, Number 5 (2011), 677-727.
Standing ring blowup solutions for cubic nonlinear Schrödinger equations
For all dimensions 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 concentration and by a bounded supercritical norm outside any neighborhood of the set. In all cases, the global norm grows at the log-log rate.
Anal. PDE, Volume 4, Number 5 (2011), 677-727.
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
Digital Object Identifier
Mathematical Reviews number (MathSciNet)
Zentralblatt MATH identifier
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B40: Asymptotic behavior of solutions
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