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Transactions of the American Mathematical Society

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The orthonormal Strichartz inequality on torus


Author: Shohei Nakamura
Journal: Trans. Amer. Math. Soc. 373 (2020), 1455-1476
MSC (2010): Primary 35B45; Secondary 35P10, 35B65
DOI: https://doi.org/10.1090/tran/7982
Published electronically: November 1, 2019
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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$ 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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Additional Information

Shohei Nakamura
Affiliation: Department of Mathematics and Information Sciences, Tokyo Metropolitan University, 1-1 Minami-Ohsawa, Hachioji, Tokyo, 192-0397, Japan
Email: nakamura-shouhei@ed.tmu.ac.jp

DOI: https://doi.org/10.1090/tran/7982
Keywords: Orthonormal Strichartz inequality on torus, periodic Hartree equation
Received by editor(s): November 5, 2018
Received by editor(s) in revised form: January 8, 2019, and August 15, 2019
Published electronically: November 1, 2019
Additional Notes: This work was supported by Grant-in-Aid for JSPS Research Fellow No. 17J01766.
Article copyright: © Copyright 2019 American Mathematical Society