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Title of Journal: Commun Math Phys

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Abbravation: Communications in Mathematical Physics

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Springer-Verlag

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DOI

10.1016/0022-0248(95)00837-3

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1432-0916

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Standing Ring Blow up Solutions to the NDimension

Authors: Pierre Raphaël Jérémie Szeftel
Publish Date: 2009/04/01
Volume: 290, Issue: 3, Pages: 973-
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Abstract

We consider the quintic nonlinear Schrödinger equation ipartial tu=Delta uu4u in dimension N ≥ 3 This problem is energy critical in dimension N = 3 and energy super critical for N ≥ 4 We prove the existence of a radially symmetric blow up mechanism with L 2 concentration along the unit sphere of mathbbRN This singularity formation is moreover stable by smooth and radially symmetric perturbation of the initial data This result extends the result obtained for N = 2 in 29 and is the first result of description of a singularity formation in the energy supercritical class for NLS type problems Our main tool is the proof of the propagation of regularity outside the blow up sphere in the presence a socalled loglog type singularity

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