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In this paper we are interested in the coupled wave and Klein-Gordonequations in $\mathbb{R}^+\times\mathbb{R}^2$. We want to establish the globalwell-posedness of such system by showing the uniform boundedness of the energyfor the global solution without any compactness assumptions on the initialdata. In addition, we also demonstrate the pointwise asymptotic behavior of thesolution pair. In order to achieve that we apply a modified Alinhac's ghostweight method together with a newly developed normal-form framework to remedythe lack of the space-time scaling vector field. Finally we show the globalsolutions scatter linearly strongly for the Klein-Gordon field $\phi$ andweakly for the wave field $n$ as $t\to+\infty$. To our best knowledge suchscattering phenomenon is novel in the literature.

Global well-posedness of a two dimensional wave-Klein-Gordon system with small non-compactly supported data