Scattering for the Klein-Gordon-Schrödinger system in three dimensions with radial data

Abstract

We prove global well-posedness and scattering for the 3D Klein-Gordon-Schrödinger system for small radial data in the best known global well-posedness range $(u_0,n_0,n_1)\in L^2\times H^{-\frac{1}{2}+\hat{I}\mu }\times H^{-\frac{3}{2}+\hat{I}\mu }$ for any $\hat{I}\mu >0$. The proof uses a global-in-time iteration scheme in the adapted function spaces $U_{\hat{I}}^2¦$, radial Strichartz estimates, and bilinear restriction estimates.

21 pages, 3 figures, 1 table