Dispersive Estimates for Nonlinear Schrödinger Equations with External Potentials
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.
 Publication:

arXiv eprints
 Pub Date:
 April 2021
 DOI:
 10.48550/arXiv.2104.05502
 arXiv:
 arXiv:2104.05502
 Bibcode:
 2021arXiv210405502D
 Keywords:

 Mathematical Physics;
 Mathematics  Analysis of PDEs;
 35Q55
 EPrint:
 31 pages, 1 figure