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Abstract
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We prove sharp pointwise kernel estimates and dispersive properties for
the linear wave equation on noncompact Riemannian symmetric spaces
of any
rank with
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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Keywords
noncompact symmetric space of higher rank, semilinear wave
equation, dispersive property, Strichartz inequality,
global well-posedness
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Mathematical Subject Classification
Primary: 22E30, 35J10, 35P25, 35L05, 43A85, 43A90, 47J35
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Milestones
Received: 23 July 2020
Accepted: 29 April 2021
Published: 31 July 2021
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