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Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data
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Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data
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eBook
Global Well-Posedness of High Dimensional Maxwell–Dirac for Small Critical Data
2020
Overview
In this paper, the authors prove global well-posedness of the massless Maxwell-Dirac equation in the Coulomb gauge on \\mathbb{R}^{1+d} (d\\geq 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.
Publisher
American Mathematical Society
Subject
ISBN
9781470441111, 147044111X
