Geodesic
Non-generic blow-up solutions for the critical focusing NLS in 1-D
Journal of the European Mathematical Society, Tome 11 (2009) no. 1, pp. 1-125 Cet article a éte moissonné depuis la source EMS Press

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We consider the L2-critical focussing nonlinear Schrödinger equation in 1+1-D. We demonstrate the existence of a large set of initial data close to the ground state soliton resulting in the pseudo-conformal type blow up behavior. More specifically, we prove a version of a conjecture of Perelman, establishing the existence of a co-dimension one stable blow up manifold in the measurable category.
DOI : 10.4171/jems/143
Classification : 35-XX, 00-XX
Keywords: Nonlinear Schrödinger equations, L2-critical NLS, pseudo-conformal blow-up 
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     author = {Joachim Krieger and Wilhelm Schlag},
     title = {Non-generic blow-up solutions for the critical focusing {NLS} in {1-D}},
     journal = {Journal of the European Mathematical Society},
     pages = {1--125},
     year = {2009},
     volume = {11},
     number = {1},
     doi = {10.4171/jems/143},
     url = {http://geodesic.mathdoc.fr/articles/10.4171/jems/143/}
}
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Joachim Krieger; Wilhelm Schlag. Non-generic blow-up solutions for the critical focusing NLS in 1-D. Journal of the European Mathematical Society, Tome 11 (2009) no. 1, pp. 1-125. doi: 10.4171/jems/143

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