2024/01/10 by Akitoshi Hoshiya, Hoshiya, Akitoshi · 4 citations
Engineering · Mathematics · #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #Electromagnetic Simulation and Numerical Methods #FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Spectral Theory in Mathematical Physics
paper · pdf · doi:10.48550/arxiv.2401.08675
openalex publication_date 2024/01/10 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
In this paper we prove the orthonormal Strichartz estimates for the higher order and fractional Schrödinger, wave, Klein-Gordon and Dirac equations with potentials. As in the case of the Schrödinger operator, the proofs are based on the smooth perturbation theory by T. Kato. However, for the Klein-Gordon and Dirac equations, we also use a method of the microlocal analysis in order to prove the estimates for wider range of admissible pairs. As applications we prove the global existence of a solution to the higher order or fractional Hartree equation with potentials which describes the dynamics of infinitely many particles. We also give a local existence result for the semi-relativistic Hartree equation with electromagnetic potentials. As another application, the refined Strichartz estimates are proved for higher order and fractional Schrödinger, wave and Klein-Gordon equations.