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Article Dans Une Revue Communications in Mathematical Physics Année : 2009

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

Résumé

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.
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Dates et versions

hal-00359368 , version 1 (06-02-2009)

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  • HAL Id : hal-00359368 , version 1

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Pierre Raphaël, Jérémie Szeftel. Standing ring blow up solutions to the N-dimensional quintic nonlinear Schrödinger equation. Communications in Mathematical Physics, 2009, A paraître. ⟨hal-00359368⟩
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