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Article Dans Une Revue Zeitschrift für Angewandte Mathematik und Physik Année : 2015

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. Zeitschrift für Angewandte Mathematik und Physik, 2015, 66 (4), pp.2087-2094. ⟨10.1007/s00033-015-0501-6⟩. ⟨hal-01066391v3⟩
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