2023/09/14 by Wang, Haoran, Zhang, Fang, Zhang, Junyong
#Analysis of PDEs (math.AP) #FOS: Mathematics #Spectral Theory (math.SP)
paper · doi:10.48550/arxiv.2309.07635
This is the first of a series of papers in which we investigate the decay estimates for dispersive equations with Aharonov-Bohm solenoids in a uniform magnetic field. In this first starting paper, we prove the local-in-time dispersive estimates and Strichartz estimates for Schrödinger equation with one Aharonov-Bohm solenoid in a uniform magnetic field. The key ingredient is the construction of Schrödinger propagator, we provide two methods to construct the propagator. The first one is combined the strategies of \citeFFFP1 and \citeGYZZ22, FZZ22, and the second one is based on the Schulman-Sunada formula in sprit of \citestov, stov1 in which the heat kernel has been studied. In future papers, we will continue investigating this quantum model for wave with one or multiple Aharonov-Bohm solenoids in a uniform magnetic field.