Differential and Integral Equations

Endpoint Strichartz estimates for magnetic wave equations on two dimensional hyperbolic spaces

Ze Li

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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 [27] and collaborative work [29] in the study of asymptotic stability of harmonic maps for wave maps from $ \mathbb R\times \mathbb H^2$ to $ \mathbb H^2$.

Article information

Source
Differential Integral Equations, Volume 32, Number 7/8 (2019), 369-408.

Dates
First available in Project Euclid: 2 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.die/1556762422

Mathematical Reviews number (MathSciNet)
MR3945761

Subjects
Primary: 58J45: Hyperbolic equations [See also 35Lxx] 58J50: Spectral problems; spectral geometry; scattering theory [See also 35Pxx]

Citation

Li, Ze. Endpoint Strichartz estimates for magnetic wave equations on two dimensional hyperbolic spaces. Differential Integral Equations 32 (2019), no. 7/8, 369--408. https://projecteuclid.org/euclid.die/1556762422


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