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Dispersive estimates for Maxwell's equations in the exterior of a sphere

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Autorschaft

  • Yan long Fang
  • Alden Waters

Organisationseinheiten

Externe Organisationen

  • University College London (UCL)

Details

OriginalspracheEnglisch
Seiten (von - bis)855-885
Seitenumfang31
FachzeitschriftJournal of differential equations
Jahrgang415
Frühes Online-Datum22 Okt. 2024
PublikationsstatusVeröffentlicht - 15 Jan. 2025

Abstract

The goal of this article is to establish general principles for high frequency dispersive estimates for Maxwell's equation in the exterior of a perfectly conducting ball. We construct entirely new generalized eigenfunctions for the corresponding Maxwell propagator. We show that the propagator corresponding to the electric field has a global rate of decay in L1−L operator norm in terms of time t and powers of h. In particular we show that some, but not all, polarizations of electromagnetic waves scatter at the same rate as the usual wave operator. The Dirichlet Laplacian wave operator L1−L norm estimate should not be expected to hold in general for Maxwell's equations in the exterior of a ball because of the Helmholtz decomposition theorem.

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Dispersive estimates for Maxwell's equations in the exterior of a sphere. / Fang, Yan long; Waters, Alden.
in: Journal of differential equations, Jahrgang 415, 15.01.2025, S. 855-885.

Publikation: Beitrag in FachzeitschriftArtikelForschungPeer-Review

Fang YL, Waters A. Dispersive estimates for Maxwell's equations in the exterior of a sphere. Journal of differential equations. 2025 Jan 15;415:855-885. Epub 2024 Okt 22. doi: 10.48550/arXiv.2308.00536, 10.1016/j.jde.2024.10.024
Fang, Yan long ; Waters, Alden. / Dispersive estimates for Maxwell's equations in the exterior of a sphere. in: Journal of differential equations. 2025 ; Jahrgang 415. S. 855-885.
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