Low regularity global well-posedness for the Klein-Gordon-Schrödinger system with the higher-order Yukawa coupling. (English) Zbl 1212.35454

Miao, Changxing; Xu, Guixiang

Differ. Integral Equ. 20, No. 6, 643-656 (2007).

Summary: 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 [Trans.Am.Math.Soc.360, No. 9, 4619-4638 (2008; Zbl 1158.35085)] to use the available \(L^2\) conservation law of \(u\) and control the growth of \(n\) via the estimates in the local theory.

MSC:

35Q55	NLS equations (nonlinear Schrödinger equations)
42B35	Function spaces arising in harmonic analysis

Keywords:

Klein-Gordon-Schrödinger system; higher-order Yukawa coupling

Citations:

Zbl 1158.35085