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

波动方程是无处不在的，研究非均匀介质中的波传播往往需要研究低正则系数的波动方程。然而，他们的数学研究仍然具有极大的挑战性。在这个项目中，我们提出了一种新的方法来计算特定的低正则波型方程和Maxwell方程组的Strichartz和色散估计，它利用了算子的结构性质并导致了改进的数量界。我们进一步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.