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

Cristian Gavrus, Sung-Jin Oh (Autoren)

Buch | Softcover

94 Seiten

2020
American Mathematical Society (Verlag)
978-1-4704-4111-1 (ISBN)

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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.

Cristian Gavrus, University of California, Berkeley, CA. Sung-Jin Oh, Korea Institute for Advanced Study, Seoul, Republic of Korea.

Erscheinungsdatum	01.04.2020
Reihe/Serie	Memoirs of the American Mathematical Society
Verlagsort	Providence
Sprache	englisch
Maße	178 x 254 mm
Gewicht	215 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Analysis
ISBN-10	1-4704-4111-X / 147044111X
ISBN-13	978-1-4704-4111-1 / 9781470441111
Zustand	Neuware