Conditional large data scattering results for the Dirac-Klein-Gordon system
Timothy Candy, Sebastian Herr
TL;DR
This paper establishes conditional global existence and scattering results for large solutions of the Dirac-Klein-Gordon system in three spatial dimensions, identifying key norms that control the system's long-term behavior.
Contribution
It introduces a new conditional framework for analyzing large solutions of the Dirac-Klein-Gordon system using refined nonlinear estimates and specific space-time Lebesgue norms.
Findings
Identification of a space-time Lebesgue norm controlling global behavior.
Conditional global existence and scattering results for large solutions.
Refined nonlinear estimates underpin the analysis.
Abstract
We obtain conditional results on the global existence and scattering for large solutions of the Dirac-Klein-Gordon system in critical spaces in dimension . In particular, for bounded solutions we identify a space-time Lebesgue norm controlling the global behaviour. The proof relies on refined nonlinear estimates involving the controlling norm.
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