Dynamics of Partial Differential Equations

Volume 16 (2019)

Number 1

Weak dispersive estimates for fractional Aharonov-Bohm-Schrödinger groups

Pages: 95 – 103

DOI: http://dx.doi.org/10.4310/DPDE.2019.v16.n1.a3

Authors

F. Cacciafesta (Dipartimento di Matematica, Università degli studi di Padova, Italy)

L. Fanelli (Dipartimento di Matematica, Sapienza Università di Roma, Italy)

Abstract

We prove local smoothing, local energy decay and weighted Strichartz inequalities for fractional Schrödinger equations with an Aharonov–Bohm magnetic field in 2D. Explicit representations of the flows in terms of spherical expansions of the Hamiltonians are involved in the study. An improvement of the free estimate is proved, when the total flux of the magnetic field through the unit sphere is not an integer.

Keywords

Schrödinger equation, magnetic potentials, local smoothing, Strichartz estimates

2010 Mathematics Subject Classification

35B99, 35J10

Full Text (PDF format)

Received 16 November 2017

Published 5 December 2018