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

Part of: Harmonic analysis in several variables Equations of mathematical physics and other areas of application

Published online by Cambridge University Press:  21 June 2018

TIMOTHY CANDY  and
SEBASTIAN HERR
TIMOTHY CANDY
Affiliation:
Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, 33501 Bielefeld, Germany; tcandy@math.uni-bielefeld.de, herr@math.uni-bielefeld.de
SEBASTIAN HERR
Affiliation:
Universität Bielefeld, Fakultät für Mathematik, Postfach 100131, 33501 Bielefeld, Germany; tcandy@math.uni-bielefeld.de, herr@math.uni-bielefeld.de

Abstract

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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.

MSC classification

Primary: 42B37: Harmonic analysis and PDE 35Q41: Time-dependent Schrödinger equations, Dirac equations

Information

Type
Research Article
Information
Forum of Mathematics, Sigma , Volume 6 , 2018 , e9
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Creative Commons
Creative Common License - CCCreative Common License - BY
This is an Open Access article, distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited.
Copyright
© The Author(s) 2018

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