Well-posedness and scattering for wave equations on hyperbolic spaces with singular data

2023/03/11 by Ferreira, Lucas C. F., Xuan, Pham Truong
#Analysis of PDEs (math.AP) #Differential Geometry (math.DG) #FOS: Mathematics #FOS: Physical sciences #Functional Analysis (math.FA) #Mathematical Physics (math-ph)

paper · doi:10.48550/arxiv.2303.06291

Abstract

We consider the wave and Klein-Gordon equations on the real hyperbolic space ℍⁿ (n ≥2) in a framework based on weak-L^p spaces. First, we establish dispersive estimates on Lorentz spaces in the context of ℍⁿ. Then, employing those estimates, we prove global well-posedness of solutions and an exponential asymptotic stability property. Moreover, we develop a scattering theory and construct wave operators in such singular framework.

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