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

Federico Cacciafesta; Zhiqing Yin; Junyong Zhang

doi:10.4310/DPDE.2022.v19.n1.a4

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

Federico Cacciafesta, Zhiqing Yin, Junyong Zhang

School of Mathematics and Statistics

Research output: Contribution to journal › Article › peer-review

2 Citations (Scopus)

Abstract

We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well estab-lished 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.

Original language	English
Pages (from-to)	71-90
Number of pages	20
Journal	Dynamics of Partial Differential Equations
Volume	19
Issue number	1
DOIs	https://doi.org/10.4310/DPDE.2022.v19.n1.a4
Publication status	Published - 2022

Keywords

Aharonov-Bohm potential
Dirac equation
Strichartz estimates
Wave equation

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10.4310/DPDE.2022.v19.n1.a4

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abstract = "We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well estab-lished 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.",

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AU - Zhang, Junyong

PY - 2022

Y1 - 2022

N2 - We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well estab-lished 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.

AB - We prove generalized Strichartz estimates for wave and massless Dirac equations in Aharonov-Bohm magnetic fields. Following a well estab-lished 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.

KW - Aharonov-Bohm potential

KW - Dirac equation

KW - Strichartz estimates

KW - Wave equation

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

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Keywords

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