Scattering for the Dirac-Klein-Gordon system with pseudoscalar source and resonant interaction

Yonggeun Cho; Changhun Yang

doi:10.4134/BKMS.b230558

Bulletin of the
Korean Mathematical Society BKMS

ISSN(Print) 1015-8634 ISSN(Online) 2234-3016

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Bull. Korean Math. Soc. 2024; 61(5): 1301-1337

Online first article September 24, 2024 Printed September 30, 2024

https://doi.org/10.4134/BKMS.b230558

Scattering for the Dirac-Klein-Gordon system with pseudoscalar source and resonant interaction

Yonggeun Cho, Changhun Yang

Jeonbuk National University; Chungbuk National University

Abstract

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Abstract

In this paper we revisit the Cauchy problems for the Dirac-Klein-Gordon system (DKG) with pseudoscalar source and resonant interaction. In the case of scalar source Candy and Herr [4-6] showed the linear scattering for small data or large data with initial data of partial smallness associated with charge conjugation. We apply their arguments to the partial smallness problem of (DKG) with pseudoscalar source and resonant interaction. We get a linear scattering result by exploiting null structure induced by chiral operator and angular regularity.

Keywords: Dirac-Klein-Gordon equation, partial smallness, linear scattering, charge conjugation, pseudoscalar source, resonant interaction

MSC numbers: Primary 35Q55, 35Q40

Supported by: The first author was supported by NRF-2021R1I1A3A04035040(Korea). The second author was supported by the National Research Foundation of Korea(NRF) grant funded by the Korea government(MSIT) (No.~2021R1C1C1005700).