Strichartz estimates for higher-order Schrödinger equations and their applications

2021/06/25 by Younghun Hong, Hong, Younghun, Chulkwang Kwak +3
Mathematics · #35Q55 #81Q05 #Advanced Mathematical Physics Problems #Analysis of PDEs (math.AP) #FOS: Mathematics #Mathematical Analysis and Transform Methods #advanced mathematical theories

paper · pdf · doi:10.48550/arxiv.2106.13483

openalex publication_date 2021/06/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

In this paper, we consider the higher-order linear Schrödinger equations, that is, a formal finite Taylor expansion of the linear pseudo-relativistic equation. We establish the 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) equation approximates the corresponding pseudo-relativistic equation on an arbitrarily long time interval, with higher accuracy than the non-relativistic equation. We also prove small data scattering for the higher-order nonlinear Schrödinger equations.

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