Differential and Integral Equations

Low regularity global well-posedness for the Klein-Gordon-Schrödinger system with the higher-order Yukawa coupling

Changxing Miao and 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 well-posedness in $L^2\times H^{1/2}$. The method to be used is adapted from the scheme originally by J. Colliander, J. Holmer, and N. Tzirakis [8] to use the available $L^2$ conservation law of $u$ and control the growth of $n$ via the estimates in the local theory.

Article information

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

Dates
First available in Project Euclid: 20 December 2012

Permanent link to this document
https://projecteuclid.org/euclid.die/1356039429

Mathematical Reviews number (MathSciNet)
MR2319459

Zentralblatt MATH identifier
1212.35454

Subjects
Primary: 35Q55: NLS-like equations (nonlinear Schrödinger) [See also 37K10]
Secondary: 35B30: Dependence of solutions on initial and boundary data, parameters [See also 37Cxx] 35B65: Smoothness and regularity of solutions 35L70: Nonlinear second-order hyperbolic equations 42B35: Function spaces arising in harmonic analysis

Citation

Miao, Changxing; Xu, Guixiang. Low regularity global well-posedness for the Klein-Gordon-Schrödinger system with the higher-order Yukawa coupling. Differential Integral Equations 20 (2007), no. 6, 643--656. https://projecteuclid.org/euclid.die/1356039429


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