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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)

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Rémi Carles. Sharp weights in the Cauchy problem for nonlinear Schrodinger equations with potential. 2014. ⟨hal-01066391v1⟩
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