Spectral methods for dispersive equations (A09)

• Subject Area: Mathematics
• Term: from 2015 to 2019
• Project identifier: Deutsche Forschungsgemeinschaft (DFG) - Project number 258734477

Spectral theory provides a unified approach to a large variety of differential operators appearing in dispersive equations. In this project we investigate spectrally localized dispersive estimates directly via the spectral data of selfadjoint operators, Gaussian bounds, and oscillatory integral representations provided by functional calculus. Moreover, we use randomizations of spectral decompositions of operators to improve classical Sobolev embeddings, aiming at well-posedness for large sets of initial data. Finally, we apply the Keel-Tao method of proving Strichartz estimates to the stochastic setting and with the goal of new well-posedness results for stochastic dispersive equations like the nonlinear Schrödinger equation.

• DFG Programme: Collaborative Research Centres
• Subproject of: SFB 1173: Wave phenomena: analysis and numerics
• Applicant Institution: Karlsruher Institut für Technologie
• Project Heads: Privatdozent Dr. Peer Christian Kunstmann; Professor Dr. Lutz Weis