On Strichartz estimates for many-body Schrödinger equation in the periodic setting

In this paper, we prove Strichartz estimates for many body Schrödinger equations in the periodic setting, specifically on tori ${\mathbb{T}}^d$, where $d\ge 3$. The results hold for both rational and irrational tori, and for small interacting potentials in a certain sense. Our work is based on the standard Strichartz estimate for Schrödinger operators on periodic domains, as developed in Bourgain-Demeter \cite{BD}. As a comparison, this result can be regarded as a periodic analogue of Hong \cite{hong2017strichartz} though we do not use the same perturbation method. We also note that the perturbation method fails due to the derivative loss property of the periodic Strichartz estimate.