CONDITIONAL LARGE INITIAL DATA SCATTERING RESULTS FOR THE DIRAC–KLEIN–GORDON SYSTEM

Abstract

We consider the global behaviour for large solutions of the Dirac–Klein–Gordon system in critical spaces in dimension $1+3$ . In particular, we show that bounded solutions exist globally in time and scatter, provided that a controlling space–time Lebesgue norm is finite. A crucial step is to prove nonlinear estimates that exploit the dichotomy between transversality and null structure, and furthermore involve the controlling norm.

Keywords

• 42B37
• 35Q41 (primary)