Decay and Strichartz estimates for dispersive equations in an Aharonov-Bohm field

Junyong Zhang, Jiqiang Zheng

Published 2020-03-06Version 1

We prove decay and Strichartz estimates for the dispersive equations with an Aharonov-Bohm potential which is a singular and scaling-critical potential. The decay estimates generalize the results of \cite{DF} and the Strichartz estimates extend the weighted Strichartz estimates for Dirac proved in \cite{CF} so that we answer the open problem raised in \cite{CF,CF1}. In addition, the argument provides a new simple proof of $L^1\to L^\infty$-decay estimate of Schr\"odinger equation shown in \cite{FFFP1}. The key point of the argument is to develop the distorted Fourier theory based on an observation of the eigenfunction of the Schr\"odinger operator with Aharonov-Bohm potential.