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Research Article | Open Access

Global solution in a weak energy class for Klein-Gordon-Schrödinger system

Qihong Shi1( ), Yaqian Jia1, Xunyang Wang1,2
Department of Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
State Grid Gansu Electric Power Research Institute, Lanzhou 730070, China
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Abstract

Based on the possible singularity of stationary state, we revisit the initial boundary value problem of the classical Klein-Gordon-Schrödinger (KGS) system in one space dimension. The wellposedness is established in a class of Sobolev NLS solutions together with exponentially growing KG solutions.

Keywords

KGS systemweak solutionglobal wellposednessenergy space

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Electronic Research Archive
Volume 30 Issue 2,
February 2022
Pages 633-643
DOI: 10.3934/era.2022033

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Cite this article:
Shi Q, Jia Y, Wang X. Global solution in a weak energy class for Klein-Gordon-Schrödinger system. Electronic Research Archive, 2022, 30(2): 633-643. https://doi.org/10.3934/era.2022033

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Received: 16 November 2021
Revised: 25 January 2022
Accepted: 15 February 2022
Published: 15 February 2022
©2022 the Author(s), licensee AIMS Press.

This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)