Dynamics of Partial Differential Equations

Volume 19 (2022)

Number 1

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

Pages: 71 – 90

DOI: https://dx.doi.org/10.4310/DPDE.2022.v19.n1.a4

Authors

Federico Cacciafesta (Dipartimento di Matematica, Universitá degli studi di Padova, Italy)

Zhiqing Yin (Department of Mathematics, Beijing Institute of Technology, Beijing, China)

Junyong Zhang (Department of Mathematics, Beijing Key Laboratory on Mathematical Characterization, Analysis, and Applications of Complex Information, Beijing Institute of Technology, Beijing, China)

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.

Keywords

Dirac equation, wave equation, Aharonov–Bohm potential, Strichartz estimates

2010 Mathematics Subject Classification

35L05, 35Q41

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Received 7 September 2021

Published 2 December 2021