We prove local smoothing, local energy decay and weighted Strichartz inequalities for fractional Schr\"odinger equations with a Aharonov-Bohm magnetic field in 2D. Explicit representations of the flows in terms of spherical expansions of the Hamiltonians are involved in the study. An improvement of the free estimate is proved, when the total flux of the magnetic field through the unit sphere is not an integer.

中文翻译：

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分数阶 Aharonov-Bohm-Schrödinger 群的弱色散估计

我们证明了具有 2D 中 Aharonov-Bohm 磁场的分数 Schr\"odinger 方程的局部平滑、局部能量衰减和加权 Strichartz 不等式。研究涉及在哈密顿量的球面扩展方面的流动的显式表示。改进当通过单位球体的磁场总通量不是整数时，证明了自由估计的 。