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arXiv 1107.0843math.AP
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一类磁Dirac流的无色散性

On the lack of dispersion for a class of magnetic Dirac flows

Naiara Arrizabalaga, Luca Fanelli, Andoni García

摘要:

我们表明,全球磁狄拉克运营商的Eschhartz估计一般失败,如果潜在的不衰减足够快,在无穷远。为了证明这一点,我们构造了一些具有小于库仑衰变的均匀磁势的显式例子,即。e.具有大于-1的磁化度,使得磁场指向固定方向,其不依赖于$x\in \mathbb{R}^3$。

英文摘要:

We show that global Strichartz estimates for magnetic Dirac operators generally fails, if the potentials do not decay fast enough at infinity. In order to prove this, we construct some explicit examples of homogeneous magnetic potentials with less than Coulomb decay, i. e. with homogeneity-degree more than -1, such that the magnetic field points to a fixed direction, which does not depend on $x\in \mathbb{R}^3$.

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