Abstract
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We consider the pointwise decay of solutions to wave-type equations
in two model singular settings. Our main result is a form of
Price’s law for solutions of the massless Dirac–Coulomb system in
-dimensions.
Using identical techniques, we prove a similar theorem for the wave equation on
Minkowski space with an inverse square potential. One novel feature of these singular
models is that solutions exhibit two different leading decay rates at timelike infinity
in two regimes, distinguished by whether the spatial momentum along a
curve which approaches timelike infinity is zero or nonzero. An important
feature of our analysis is that it yields a precise description of solutions
at the interface of these two regions which comprise the whole of timelike
infinity.
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Keywords
Price's law, Dirac–Coulomb
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Mathematical Subject Classification
Primary: 35L05, 35L81, 35Q41
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Milestones
Received: 10 April 2023
Revised: 5 March 2025
Accepted: 20 March 2025
Published: 18 April 2025
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