Dispersive estimates for wave-type equations with low regularity coefficients (A13#)

波动方程是普遍存在的，并且例如在非均匀介质中的波传播的研究通常需要研究具有低正则性系数的波动方程。然而，他们的数学研究仍然极具挑战性。在这个项目中，我们提出了一种新的方法来具体的低正则性波型方程和麦克斯韦系统，利用运营商的结构特性，并导致改进的定量界的Khartz和色散估计。我们还考虑了具有大磁势的薛定谔算子。

Wave equations are ubiquitous, and the investigation of e.g. wave propagation in inhomogeneous media often requires the study of wave equations with low regularity coefficients. Yet the their mathematical investigation remains highly challenging. In this project we propose a new approach to Strichartz and dispersive estimates for specific low regularity wave-type equations and Maxwell systems, which exploits structural properties of the operators and leads to improved quantitative bounds. We furthermore consider Schrödinger operators with large magnetic potentials.