Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data PDF Download

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Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data

Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data PDF Author: Cristian Gavrus
Publisher: American Mathematical Soc.
ISBN: 147044111X
Category : Education
Languages : en
Pages : 106

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Book Description
In this paper, the authors prove global well-posedness of the massless Maxwell–Dirac equation in the Coulomb gauge on R1+d(d≥4) for data with small scale-critical Sobolev norm, as well as modified scattering of the solutions. Main components of the authors' proof are A) uncovering null structure of Maxwell–Dirac in the Coulomb gauge, and B) proving solvability of the underlying covariant Dirac equation. A key step for achieving both is to exploit (and justify) a deep analogy between Maxwell–Dirac and Maxwell-Klein-Gordon (for which an analogous result was proved earlier by Krieger-Sterbenz-Tataru, which says that the most difficult part of Maxwell–Dirac takes essentially the same form as Maxwell-Klein-Gordon.