Dispersive estimates for nonlinear Schrödinger equations with external potentials
- 1 November 2021
- journal article
- research article
- Published by AIP Publishing in Journal of Mathematical Physics
- Vol. 62 (11), 111502
- https://doi.org/10.1063/5.0055911
Abstract
We consider the long time dynamics of nonlinear Schrödinger equations with an external potential. More precisely, we look at Hartree type equations in three or higher dimensions with small initial data. We prove an optimal decay estimate, which is comparable to the decay of free solutions. Our proof relies on good control on a high Sobolev norm of the solution to estimate the terms in Duhamel’s formula.Funding Information
- Deutsche Forschungsgemeinschaft (426365943)
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