This paper is devoted to study the dispersive properties of the linear Klein-Gordon and wave equations on a class of locally symmetric spaces. As a consequence, we obtain the Strichartz estimate and prove global wellposedness results for the corresponding semilinear equation with low regularity data as on real hyperbolic spaces.2000 Mathematics Subject Classification. 35Q55, 43A85, 22E30, 35P25, 47J35, 58D25.
In this paper, we prove sharp pointwise kernel estimates and dispersive properties for the linear wave equation on noncompact Riemannian symmetric spaces G/K 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. 2020 Mathematics Subject Classification. 22E30, 35J10, 35P25, 43A85, 43A90. Key words and phrases. noncompact symmetric space of higher rank, semilinear wave equation, dispersive property, Strichartz inequality, global well-posedness.1 The symbol , let us recall, means precisely that there exists a constant 0 < C < +∞ such that, wherep is the dual exponent of p, defined by the formula 1 p + 1 p = 1, and similarly forq .
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