Strichartz Estimates for 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 $n\ge 3$. Finally, in the last section, we discuss the extension of these results to matrix charge transfer models in ${\mathbb{R}}^3$.

26 pages, this is a revised version based on the comments of an anonymous referee

References in corpus (1)

• Fine properties of Charge Transfer Models

Cited by in corpus (2)

• Strichartz Estimates for Wave equations with Charge Transfer Hamiltonian
• Soliton-potential interactions for nonlinear Schrödinger equation in ${\mathbb{R}}^3$