Strichartz estimates for higher-order Schr\"odinger equations and their applications

Younghun Hong; Chulkwang Kwak; Changhun Yang

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arXiv · 2106.13483

Strichartz estimates for higher-order Schr\"odinger equations and their applications

Younghun Hong·Chulkwang Kwak·Changhun Yang

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Abstract

In this paper, we consider the higher-order linear Schr\"odinger 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 Schr\"odinger equations.

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Younghun Hong, Chulkwang Kwak, Changhun Yang. 2021-06-25. Strichartz estimates for higher-order Schr\"odinger equations and their applications. https://arxiv.org/abs/2106.13483

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