CONDITIONAL LARGE INITIAL DATA SCATTERING RESULTS FOR THE DIRAC–KLEIN–GORDON SYSTEM. (21st June 2018) - CANDY, TIMOTHY; HERR, SEBASTIAN
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.