Year: 2025
Type: article
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.The authors are grateful to Peter Hintz and Andras Vasy for helpful conversations at various points regarding the relationship between radiation fields and Price's law.
Source: Pacific Journal of Mathematics
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Awards: Algorithms and Analysis for Models in Materials Science, Fluids, and Probability, G2482512751, Mathematical Sciences Research Institute (MSRI), G2599005893, G329468232, CAREER: Wave evolution on singular spacetimes, G6019427330, Singular spaces in analysis and geometry, Global wavefront propagation and non-elliptic Fredholm theory, G6671297155
OpenAlex ID: W4409589626