Low-regularity global well-posedness for the Klein-Gordon-Schrödinger system on R⁺

In this paper we establish an almost optimal well–posedness and regularity theory for the Klein-Gordon-Schrödinger system on the half line. In particular we prove local-in-time well–posedness for rough initial data in Sobolev spaces of negative indices. Our results are consistent with the sharp well–posedness results that exist in the full line case and in this sense appear to be sharp. Finally we prove a global well–posedness result by combining the L ² conservation law of the Schrödinger part with a careful iteration of the rough wave part in lower order Sobolev norms in the spirit of the work in [5].