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Pré-publication, Document de travail Année : 2014

Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential

Résumé

We review different properties related to the Cauchy problem for the (nonlinear) Schrodinger equation with a smooth potential. For energy-subcritical nonlinearities and at most quadratic potentials, we investigate the necessary decay in space in order for the Cauchy problem to be locally (and globally) well-posed. The characterization of the minimal decay is different in the case of super-quadratic potentials.
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Dates et versions

hal-01066391, version 1 (19-09-2014)
hal-01066391, version 2 (23-09-2014)
hal-01066391, version 3 (01-10-2014)

Identifiants

  • HAL Id : hal-01066391 , version 2
  • ARXIV : 1409.5759

Citer

Rémi Carles. Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential. 2014. ⟨hal-01066391v2⟩
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Dernière date de mise à jour le 25/06/2024
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