Orthonormal Strichartz estimate for dispersive equations with potentials
Abstract
In this paper we prove the orthonormal Strichartz estimates for the higher order and fractional Schr\"odinger, wave, Klein-Gordon and Dirac equations with potentials. As in the case of the Schr\"odinger 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 Schr\"odinger, wave and Klein-Gordon equations.
Cite
@article{arxiv.2401.08675,
title = {Orthonormal Strichartz estimate for dispersive equations with potentials},
author = {Akitoshi Hoshiya},
journal= {arXiv preprint arXiv:2401.08675},
year = {2024}
}