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Endpoint Strichartz estimates for magnetic wave equations on two dimensional hyperbolic spaces. (English) Zbl 1463.35133

Author’s abstract: In this paper, we prove that the Kato smoothing effects for magnetic half wave operators can yield the endpoint Strichartz estimates for linear wave equations with magnetic potentials on the two dimensional hyperbolic spaces. As a corollary, we obtain the endpoint Strichartz estimates in the case of small potentials. This result serves as a cornerstone for the author’s work [Adv. Math. 370, Article ID 107234, 86 p. (2020; Zbl 1441.35040)] and collaborative work [Z. Li et al., Dyn. Partial Differ. Equ. 15, No. 4, 283–336 (2018; Zbl 1404.35292)] in the study of asymptotic stability of harmonic maps for wave maps from \(\mathbb{R}\times\mathbb{H}^2\) to \(\mathbb{H}^2\).

MSC:

35B45 A priori estimates in context of PDEs
35L05 Wave equation
35L15 Initial value problems for second-order hyperbolic equations
58J45 Hyperbolic equations on manifolds
58J50 Spectral problems; spectral geometry; scattering theory on manifolds
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