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

TL;DR

This paper establishes global well-posedness and scattering for the 3D Klein-Gordon-Schrödinger system with small radial data, using advanced function spaces and estimates to extend the known results.

Contribution

It proves the best known global well-posedness range for small radial data in the 3D Klein-Gordon-Schrödinger system, employing a novel iteration scheme and specialized estimates.

Findings

Proves global well-posedness for small radial data in the specified function spaces.

Establishes scattering results for the system under these conditions.

Utilizes radial Strichartz and bilinear restriction estimates to achieve results.

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.