RAPHAËL, Pierre; SZEFTEL, Jérémie

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RAPHAËL, Pierre
Institut de Mathématiques de Toulouse UMR5219 [IMT]

SZEFTEL, Jérémie
Laboratoire de Mathématiques Appliquées de Bordeaux [MAB]
Institut de Mathématiques de Bordeaux [IMB]

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Communications in Mathematical Physics. 2009p. A paraître

Springer Verlag

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We consider the quintic nonlinear Schr ̈odinger equation in dimension N ≥ 3. This problem is energy critical in dimension N = 3 and energy super critical for N ≥ 4. We prove the existence of a radially symmetric blow up mechanism with L2 concentration along the unit sphere of RN . This singularity formation is moreover stable by smooth and radially symmetric perturbation of the initial data. This result extends the result obtained for N = 2 in [29] and is the first result of description of a singularity formation in the energy supercritical class for (NLS) type problems. Our main tool is the proof of the propagation of regularity outside the blow up sphere in the presence a so-called log-log type singularity.< Leer menos

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Standing ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation

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