Strichartz estimates for higher-order Schrödinger equations and their applications

Younghun Hong, Chulkwang Kwak, Changhun Yang

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Abstract

We consider the higher-order linear Schrödinger equations which are formal finite Taylor expansions of the linear pseudo-relativistic Schrödinger equation. In this paper, we establish global-in-time Strichartz estimates for these higher-order equations which hold uniformly in the speed of light. As nonlinear applications, we show that the higher-order Hartree(-Fock) equations approximate the corresponding pseudo-relativistic equation on an arbitrarily long time interval, with higher accuracy than the non-relativistic model. We also prove small data scattering for the higher-order nonlinear Schrödinger equations.

Original languageEnglish
Pages (from-to)41-75
Number of pages35
JournalJournal of Differential Equations
Volume324
DOIs
StatePublished - 5 Jul 2022

Bibliographical note

Funding Information:
This research of the first author was supported by the Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Science and ICT (NRF-2020R1A2C4002615). C. K. was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A0106876811). C. Yang was supported by the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2021R1C1C1005700).

Publisher Copyright:
© 2022 Elsevier Inc.

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