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 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.

Keywords
focusing, nonlinear Schrödinger equation, supercritical, collapse, blowup rate, blowup set, codimension, regularity, log-log rate
Mathematical Subject Classification 2000
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