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

In this paper, we prove Strichartz estimates for many body Schrodinger equations in the periodic setting, specifically on tori T-d, where d >= 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 Schrodinger operators on periodic domains, as developed in [J. Bourgain and C. Demeter, The proof of the l(2) decoupling conjecture, Ann. of Math. (2) 182 (2015), no. 1, 351-389]. As a comparison, this result can be regarded as a periodic analogue of [Y. Hong, Strichartz estimates for N-body Schrodinger operators with small potential interactions, Discrete Contin. Dyn. Syst. 37 (2017), no. 10, 5355-5365] 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.