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

Joachim Krieger·Wilhelm Schlag
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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.

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Joachim Krieger, Wilhelm Schlag. 2005-08-29. Non-generic blow-up solutions for the critical focusing NLS in 1-d. https://arxiv.org/abs/math/0508576

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