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Price's law for the massless Dirac–Coulomb system

Dean Baskin, Jesse Gell-Redman and Jeremy L. Marzuola

Vol. 335 (2025), No. 2, 211–227
Abstract

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 (3+1)-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.

Keywords
Price's law, Dirac–Coulomb
Mathematical Subject Classification
Primary: 35L05, 35L81, 35Q41
Milestones
Received: 10 April 2023
Revised: 5 March 2025
Accepted: 20 March 2025
Published: 18 April 2025
Authors
Dean Baskin
Department of Mathematics
Texas A&M University
College Station, TX
United States
Jesse Gell-Redman
School of Mathematics and Statistics
University of Melbourne
Melbourne
Australia
Jeremy L. Marzuola
Department of Mathematics
University of North Carolina at Chapel Hill
Chapel Hill, NC
United States

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