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

Research output: Contribution to journalArticleResearchpeer review

Authors

  • Yan long Fang
  • Alden Waters

Research Organisations

External Research Organisations

  • University College London (UCL)
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Details

Original languageEnglish
Pages (from-to)855-885
Number of pages31
JournalJournal of differential equations
Volume415
Early online date22 Oct 2024
Publication statusPublished - 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.

Keywords

    Dispersive estimates, Maxwell's equations

ASJC Scopus subject areas

Cite this

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

Research output: Contribution to journalArticleResearchpeer 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 Oct 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 ; Vol. 415. pp. 855-885.
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