Generalized Strichartz estimates for wave and Dirac equations in Aharonov-Bohm magnetic fields

TL;DR

This paper establishes generalized Strichartz estimates for wave and Dirac equations in Aharonov-Bohm magnetic fields, using Hankel transforms and Bessel function estimates, and also proves a local smoothing estimate for Klein-Gordon equations.

Contribution

It introduces new generalized Strichartz estimates for dispersive PDEs in Aharonov-Bohm magnetic fields, extending previous results with novel analytical techniques.

Findings

Proved generalized Strichartz estimates for wave and Dirac equations in Aharonov-Bohm fields.

Established a local smoothing estimate for Klein-Gordon equations in the same magnetic setting.

Utilized Hankel transform and Bessel function estimates to handle scaling critical perturbations.

Abstract

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well established strategy to deal with scaling critical perturbations of dispersive PDEs, we make use of Hankel transform and rely on some precise estimates on Bessel functions. As a complementary result, we prove a local smoothing estimate for the Klein-Gordon equation in the same magnetic field.