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In this paper, we prove Strichartz estimates for N-body Schr\"odingerequations in the periodic setting, specifically on tori $\mathbb{T}^d$, where$d\geq 3$. The results hold for both rational and irrational tori, and forsmall interacting potentials in a certain sense. Our work is based on thestandard Strichartz estimate for Schr\"odinger operators on periodic domains,as developed by Bourgain-Demeter \cite{BD}, and can also be extended to thewaveguide case using Barron's recent result \cite{Barron}. This result can beregarded as a periodic analogue of Hong \cite{hong2017strichartz}.

On Strichartz estimates for many-body Schr\"odinger equation in the periodic setting