The orthonormal Strichartz inequality on torus
Shohei Nakamura

TL;DR
This paper establishes sharp orthonormal system Strichartz inequalities on the torus and applies them to prove well-posedness for the periodic Hartree equation involving infinitely many quantum particles.
Contribution
It introduces sharp orthonormal system Strichartz inequalities on the torus and demonstrates their application to quantum many-body problems.
Findings
Sharp estimates for orthonormal system Strichartz inequalities on the torus.
Application to well-posedness of the periodic Hartree equation.
Extension of recent works by Frank-Lewin-Lieb-Seiringer and Frank-Sabin.
Abstract
In this paper, motivated by recent important works due to Frank-Lewin-Lieb-Seiringer \cite{FLLS} and Frank-Sabin \cite{frank-sabin-1}, we study the Strichartz inequality on torus with the orthonormal system input and obtain sharp estimates in certain sense. An application of the inequality shows the well-posedness to the periodic Hartree equation describing the infinitely many quantum particles with the power type interaction.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · advanced mathematical theories · Mathematical Analysis and Transform Methods
