Strichartz estimates for higher-order Schrödinger equations and their applications

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. © 2022 Elsevier Inc.