Non-generic blow-up solutions for the critical focusing NLS in 1-d

Preprint

29 August 2005

preprint
Published by arXiv in arXiv

https://doi.org/10.48550/arXiv.math/0508576

Abstract

This paper addresses the existence of codimension one stable manifolds for the pseudo-conformal blow-up solution for critical one-dimensional NLS. By the work of Perelman and Merle, Raphael, the blow-up rate of these solutions is far from the generic one. However, Bourgain,Wang and Perelman formulated the possibility of codimension one stable manifolds for the non-generic blow-up solutions. This paper established the existence of such manifolds, albeit only in the measurable category.

Keywords

CRITICAL FOCUSING
BLOW UP SOLUTIONS
STABLE MANIFOLDS
GENERIC BLOW
FOCUSING NLS
CODIMENSION
PERELMAN
NLS

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Version 1, 2005-08-29, ArXiv

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