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

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

Zbl 1158.35085
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