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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The orthonormal Strichartz inequality on torus
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by Shohei Nakamura PDF
Trans. Amer. Math. Soc. 373 (2020), 1455-1476 Request permission

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
  • MR Author ID: 1145908
  • Email: nakamura-shouhei@ed.tmu.ac.jp
  • 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.
  • © Copyright 2019 American Mathematical Society
  • Journal: Trans. Amer. Math. Soc. 373 (2020), 1455-1476
  • MSC (2010): Primary 35B45; Secondary 35P10, 35B65
  • DOI: https://doi.org/10.1090/tran/7982
  • MathSciNet review: 4068269