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

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

2006-06-04

arxiv.org/abs/math/0606079v2

Differential and Integral Equations Volume 20, Number 6(2007)643-656

Mathematics

Analysis of PDEs

13 pages, 3 figures

Scientific paper

In this paper, we consider the Klein-Gordon-Schr\"{o}dinger 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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