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

Qihong Shi; Yaqian Jia; Xunyang Wang; Qihong Shi; Yaqian Jia; Xunyang Wang

doi:10.3934/era.2022033

Electronic Research Archive

2022, Volume 30, Issue 2: 633-643. doi: 10.3934/era.2022033

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

1.
Department of Mathematics, Lanzhou University of Technology, Lanzhou 730050, China
2.
State Grid Gansu Electric Power Research Institute, Lanzhou 730070, China

Academic Editor: Alain Miranville

Received: 16 November 2021 Revised: 25 January 2022 Accepted: 15 February 2022 Published: 17 February 2022

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.
- KGS system,
- weak solution,
- global wellposedness,
- energy space
Citation: Qihong Shi, Yaqian Jia, Xunyang Wang. Global solution in a weak energy class for Klein-Gordon-Schrödinger system[J]. Electronic Research Archive, 2022, 30(2): 633-643. doi: 10.3934/era.2022033

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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.

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