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Low Regularity Global Well-Posedness for the Klein-Gordon-Schrödinger System with the Higher Order Yukawa Coupling

Changxing Miao·Guixiang Xu
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Abstract

In this paper, we consider the Klein-Gordon-Schrödinger system with the higher order Yukawa coupling in $ \mathbb{R}^{1+1} $, and prove the local and global wellposedness in $L^2\times H^{1/2}$. The method to be used is adapted from the scheme originally by Colliander J., Holmer J., Tzirakis N. \cite{CoHT06} to use the available $L^2$ conservation law of $u$ and control the growth of $n$ via the estimates in the local theory.

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Changxing Miao, Guixiang Xu. 2006-06-08. Low Regularity Global Well-Posedness for the Klein-Gordon-Schrödinger System with the Higher Order Yukawa Coupling. https://arxiv.org/abs/math/0606079

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