Global well-posedness of high dimensional Maxwell-Dirac for small critical data
著者
書誌事項
Global well-posedness of high dimensional Maxwell-Dirac for small critical data
（Memoirs of the American Mathematical Society, no. 1279）
American Mathematical Society, c2020
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注記
"March 2020, volume 264, number 1279 (second of 6 numbers)"
Includes bibliographical reference (p. 93-94)
内容説明・目次
内容説明
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.
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