Aharonov-Bohm磁场中波动方程和狄拉克方程的广义Strichartz估计

IF 1.1 3区数学 Q2 MATHEMATICS, APPLIED

Dynamics of Partial Differential Equations Pub Date : 2020-08-01 DOI:10.4310/dpde.2022.v19.n1.a4

F. Cacciafesta, Zhiqing Yin, Junyong Zhang

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引用次数: 3

摘要

我们证明了Aharonov-Bohm磁场中波动和无质量Dirac方程的广义Strichartz估计。根据一个很好的策略来处理色散偏微分方程的标度临界扰动，我们利用Hankel变换，并依赖于贝塞尔函数的一些精确估计。作为一个补充结果，我们证明了在相同磁场中Klein-Gordon方程的局部平滑估计。

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

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.

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来源期刊

Dynamics of Partial Differential Equations 数学-应用数学

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： Publishes novel results in the areas of partial differential equations and dynamical systems in general, with priority given to dynamical system theory or dynamical aspects of partial differential equations.