The wave equation on Damek-Ricci spaces
Jean-Philippe Anker (MAPMO), Vittoria Pierfelice (MAPMO), Maria, Vallarino
TL;DR
This paper investigates the dispersive behavior of the wave equation on Damek-Ricci spaces, deriving Strichartz estimates and establishing global well-posedness for nonlinear cases.
Contribution
It provides the first analysis of wave equations on Damek-Ricci spaces, including dispersive estimates and global well-posedness results.
Findings
Derived Strichartz estimates for the wave equation on Damek-Ricci spaces
Established global well-posedness for nonlinear wave equations in this setting
Extended analysis to a broad class of admissible pairs
Abstract
We study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on Damek-Ricci spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain global well-posedness results for the nonlinear wave equation.
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Taxonomy
TopicsAdvanced Mathematical Physics Problems · Advanced Harmonic Analysis Research · Mathematical Analysis and Transform Methods