Strichartz estimates for $N$-body Schrödinger operators with small potential interactions

Younghun Hong

doi:10.3934/dcds.2017233

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2017, Volume 37, Issue 10: 5355-5365. Doi: 10.3934/dcds.2017233

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Strichartz estimates for $N$-body Schrödinger operators with small potential interactions

Younghun Hong^,

Center for Mathematical Analysis & Computation (CMAC), Yonsei University, Seoul 03722, Korea

* Corresponding author: Younghun Hong
* Corresponding author: Younghun Hong

Received: December 31, 2015

Revised: April 30, 2017

Published: October 2017

The author is supported by NRF grant 2015R1A5A1009350

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Abstract

In this paper, we prove Strichartz estimates for $N$-body Schrödinger operators, provided that interaction potentials are small enough. Our tools are new Strichartz estimates with frozen spatial variables, and its improvement in the $V_S^p$-norm of Koch and Tataru [19]. As an application, we prove scattering for $N$-body Schrödinger operators.

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Mathematics Subject Classification: Primary: 35Q40, 35Q41, 81U10; Secondary: 35B40, 35Q70.

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