Strichartz Estimates for Charge Transfer Models

TL;DR

This paper establishes Strichartz estimates for scalar charge transfer models in three-dimensional space, demonstrating bounded energy evolution and extending results to higher dimensions and matrix models.

Contribution

It provides new proofs of Strichartz estimates for charge transfer models without phase space methods and extends these results to matrix models in three dimensions.

Findings

Proved Strichartz estimates for scalar charge transfer models in R^3.

Showed energy boundedness independently of time.

Extended results to matrix charge transfer models.

Abstract

In this note, we prove Strichartz estimates for scattering states of scalar charge transfer models in $\mathbb{R}^{3}$. Based on the idea of the proof of Strichartz estimates which follows \cite{CM,RSS}, we also show the energy of the whole evolution is bounded independently of time without using the phase space method, for example, in \cite{Graf}. One can easily generalize our argument to $\mathbb{R}^{n}$ for $n\geq3$. Finally, in the last section, we discuss the extension of these results to matrix charge transfer models in $\mathbb{R}^{3}$.