CONDITIONAL LARGE INITIAL DATA SCATTERING RESULTS FOR THE DIRAC–KLEIN–GORDON SYSTEM. (21st June 2018)

• Record Type: Journal Article
• Authors: CANDY, TIMOTHY; HERR, SEBASTIAN
• Is Part Of: Forum of mathematics. Volume 6(2018)
• Publication Date: 2018-06-21
• Subjects: 42B37, -- 35Q41 (primary); Mathematics -- Periodicals; 510
• DOI: 10.1017/fms.2018.8
• Languages: English
• ISSNs: 2050-5094

Abstract

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.