Details
Original language | English |
---|---|
Pages (from-to) | 855-885 |
Number of pages | 31 |
Journal | Journal of differential equations |
Volume | 415 |
Early online date | 22 Oct 2024 |
Publication status | Published - 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
- Mathematics(all)
- Analysis
- Mathematics(all)
- Applied Mathematics
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In: Journal of differential equations, Vol. 415, 15.01.2025, p. 855-885.
Research output: Contribution to journal › Article › Research › peer review
}
TY - JOUR
T1 - Dispersive estimates for Maxwell's equations in the exterior of a sphere
AU - Fang, Yan long
AU - Waters, Alden
N1 - Publisher Copyright: © 2024 The Author(s)
PY - 2025/1/15
Y1 - 2025/1/15
N2 - 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.
AB - 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.
KW - Dispersive estimates
KW - Maxwell's equations
UR - http://www.scopus.com/inward/record.url?scp=85206916825&partnerID=8YFLogxK
U2 - 10.48550/arXiv.2308.00536
DO - 10.48550/arXiv.2308.00536
M3 - Article
AN - SCOPUS:85206916825
VL - 415
SP - 855
EP - 885
JO - Journal of differential equations
JF - Journal of differential equations
SN - 0022-0396
ER -