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Dispersive and Strichartz estimates for 3D wave equation with a Laguerre potential

Part of: Equations of mathematical physics and other areas of application Harmonic analysis in several variables Hyperbolic equations and systems

Published online by Cambridge University Press:  07 March 2024

Haoran Wang
Haoran Wang*
Affiliation:
Department of Mathematics, Beijing Institute of Technology, Beijing 100081, China
*
e-mail: [email protected]
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Abstract

Dispersive and Strichartz estimates are obtained for solutions to the wave equation with a Laguerre potential in spatial dimension three. To obtain the desired dispersive estimate, based on the spectral properties of the Schrödinger operator involved, we subsequently prove the dispersive estimate for the corresponding Schrödinger semigroup, obtain a Gaussian-type upper bound, establish Bernstein-type inequalities, and finally pass to the Müller–Seeger’s subordination formula. The desired Strichartz estimates follow by the established dispersive estimate and the standard argument of Keel–Tao.

Keywords

Dispersive estimateStrichartz estimatewave equationLaguerre potential

MSC classification

Primary: 42B37: Harmonic analysis and PDE 35L05: Wave equation 35Q40: PDEs in connection with quantum mechanics
Type
Article
Information
Canadian Journal of Mathematics , First View , pp. 1 - 28
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Copyright
© The Author(s), 2024. Published by Cambridge University Press on behalf of Canadian Mathematical Society

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