#### Vol. 4, No. 5, 2011

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Standing ring blowup solutions for cubic nonlinear Schrödinger equations

### Ian Zwiers

Vol. 4 (2011), No. 5, 677–727
##### Abstract

For all dimensions $N\ge 3$ 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 ${L}^{2}$ concentration and by a bounded supercritical norm outside any neighborhood of the set. In all cases, the global ${H}^{1}$ norm grows at the log-log rate.

##### Keywords
focusing, nonlinear Schrödinger equation, supercritical, collapse, blowup rate, blowup set, codimension, regularity, log-log rate
Primary: 35Q55
Secondary: 35B40
##### Milestones
Received: 5 February 2010
Revised: 27 September 2010
Accepted: 14 November 2010
Published: 16 February 2012

Proposed: Frank Merle
##### Authors
 Ian Zwiers Department of Mathematics University of British Columbia Vancouver, V6T 1Z2 Canada