The wave equation on hyperbolic spaces
Jean-Philippe Anker (MAPMO), Vittoria Pierfelice (MAPMO), Maria, Vallarino (POLITO)
TL;DR
This paper investigates the dispersive behavior of the wave equation on hyperbolic spaces, deriving Strichartz estimates and establishing local well-posedness for nonlinear variants.
Contribution
It introduces new dispersive estimates for the wave equation on hyperbolic spaces and applies them to nonlinear wave equations, extending existing results.
Findings
Derived Strichartz estimates for wave equations on hyperbolic spaces
Established local well-posedness for nonlinear wave equations in this setting
Analyzed dispersive properties of the shifted Laplace-Beltrami operator
Abstract
In this paper, we study the dispersive properties of the wave equation associated with the shifted Laplace-Beltrami operator on real hyperbolic spaces, and deduce Strichartz estimates for a large family of admissible pairs. As an application, we obtain local well-posedness results for the nonlinear wave equation.
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