Lucas C. F. Ferreira

Universidade de Campinas, Brazil

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

Abstract: We consider the wave and Klein-Gordon equations on the real hyperbolic space Hn (n ≥ 2) in a framework based on weak-Lp 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. Joint work with Prof. Pham T. Xuan (HUST, Vietnam).