Vol. 3, No. 2, 2021

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Wave equation on certain noncompact symmetric spaces

Hong-Wei Zhang

Vol. 3 (2021), No. 2, 363–386

We prove sharp pointwise kernel estimates and dispersive properties for the linear wave equation on noncompact Riemannian symmetric spaces GK of any rank with G complex. As a consequence, we deduce Strichartz inequalities for a large family of admissible pairs and prove global well-posedness results for the corresponding semilinear equation with low-regularity data as on hyperbolic spaces.

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noncompact symmetric space of higher rank, semilinear wave equation, dispersive property, Strichartz inequality, global well-posedness
Mathematical Subject Classification
Primary: 22E30, 35J10, 35P25, 35L05, 43A85, 43A90, 47J35
Received: 23 July 2020
Accepted: 29 April 2021
Published: 31 July 2021
Hong-Wei Zhang
Department of Mathematics: Analysis, Logic and Discrete Mathematics
Ghent University
Institut Denis Poisson
Université d’Orléans, Université de Tours & CNRS