Scattering for the Klein-Gordon-Schr\"odinger system in three dimensions with radial data

Abstract

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