English

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

Analysis of PDEs 2007-05-23 v1 Mathematical Physics math.MP

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

Cite

@article{arxiv.math/0508576,
  title  = {Non-generic blow-up solutions for the critical focusing NLS in 1-d},
  author = {Joachim Krieger and Wilhelm Schlag},
  journal= {arXiv preprint arXiv:math/0508576},
  year   = {2007}
}