Abstract
In this paper, motivated by recent works due to Frank-Lewin-Lieb-Seiringer and Frank-Sabin, we study the Strichartz inequality on torus with the orthonormal system input and obtain sharp estimates in a certain sense. In particular, we will reveal the tradeoff relation between Sobolev regularity and Schatten exponent gain where the 1 / p 1/p derivative-loss Strichartz inequality plays an important role as in the context on compact manifold due to Burq-Gérard-Tzvetkov. An application of the inequality shows the local well-posedness to the periodic Hartree equation describing the infinitely many quantum particles interacting with the power type potential.
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