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

Cristian-Dan Gavrus (Autor)

eBook Download: PDF

94 Seiten
American Mathematical Society (Verlag)
978-1-4704-5808-9 (ISBN)

Infos

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.

Produkt-Details

• Themenwelt: Mathematik / Informatik ► Mathematik ► Analysis
• Themenwelt: Mathematik / Informatik ► Mathematik ► Angewandte Mathematik
• ISBN-10: 1-4704-5808-X / 147045808X
• ISBN-13: 978-1-4704-5808-9 / 9781470458089