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

• Autores: J. Krieger, Wilhelm Schlag
• Localización: Journal of the European Mathematical Society, ISSN 1435-9855, Vol. 11, Nº 1, 2009, págs. 1-126
• Idioma: inglés
• DOI: 10.4171/jems/143
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• Resumen

  • 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