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Long range scattering for the Maxwell–Schrödinger system in the Lorenz gauge without any restriction on the size of data

Liu Yang 和田 健志 島根大学 DOI:10.1016/j.jde.2020.02.013

2020.08.05

概要

This paper concerns the scattering theory for the Maxwell–Schrödinger (MS) system in the Lorenz gauge, or more precisely, the existence of the modified wave operators for this system in R3+1 space-time. We construct solutions to the MS system which behave as free Maxwell and Schrödinger waves with prescribed asymptotic states when t → ∞, without any restriction on the size thereof. Since this system belongs to the borderline between the short range case and the long range case, we need modification of phase for the Schrödinger function.

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YANG LIU AND TAKESHI WADA

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School of Mathematics and Statistics, and Center for Mathematics and Interdisciplinary

Sciences, Northeast Normal University, Changchun, Jilin 130024, PR China

LONG RANGE SCATTERING FOR THE MAXWELL–SCHRODINGER

SYSTEM

61

Double Degree Program, Mathematics Course, Interdisciplinary Graduate School of Science and Engineering, Shimane University, Matsue 690-8504, Japan

E-mail address: liuy694@nenu.edu.cn

Department of Mathematics, Shimane University, Matsue 690-8504, Japan

E-mail address: wada@riko.shimane-u.ac.jp

...

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