Academy of Mathematics and Systems Science, CAS
Colloquia & Seminars
| | Speaker: | 郑继强，北京应用物理与计算数学研究所
| | Inviter: | | Title:
| Dispersive and Strichartz estimate for dispersive equations with scaling -critical electromagnetic potential | Time & Venue:
| 2021.09.24 16:00-17:00 南楼N913室 | Abstract:
| In this talk, We study the dispersive equation with Aharonov-Bohm magnetic potential. We prove sharp time-decay estimates in the purely magnetic case, and Strichartz estimates for the complete model, involving a critical electromagnetic field. The novel ingredients are the Schwartz kernels of the spectral measure and heat propagator of the Schr?dinger operator in Aharonov-Bohm magnetic fields. In particular, we explicitly construct the representation of the spectral measure and resolvent of the Schr?dinger operator with Aharonov-Bohm potentials, and show that the heat kernel in critical electromagnetic fields satisfies Gaussian boundedness. This talk is based on a series of joint works with Xiaofen Gao, Luca Fanelli, Zhiqing Yin and Junyong Zhang.
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