Strichartz estimates for higher-order Schrödinger equations and their applications

Younghun Hong, Chulkwang Kwak, Changhun Yang

Research output: Contribution to journalArticlepeer-review


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
StatePublished - 5 Jul 2022


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