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

低正则系数波动型方程的色散估计（A13

• 批准号: 462315506
• 金额: --
• 依托单位: Arbeitsgruppe Funktionalanalysis
• 依托单位国家: 德国
• 项目类别: Collaborative Research Centres
• 资助国家: 德国
• 项目状态: 未结题
• 来源: https://gepris.dfg.de/gepris/projekt/462315506?language=en
• 关键词: Dispersive; estimates; wave; type; equations

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.

波动方程是普遍存在的，例如，研究波在非均匀介质中的传播往往需要研究具有低正则系数的波动方程。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对特定的低正则波型方程和麦克斯韦系统的Strichartz和色散估计，它利用了算子的结构性质，并导致改进的定量界限。我们进一步考虑具有大磁势的Schrödinger算符。