Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds

Junyong Zhang

doi:10.1016/j.aim.2014.11.013

Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds

Junyong Zhang^*

^*Corresponding author for this work

School of Mathematics and Statistics

Australian National University

Research output: Contribution to journal › Article › peer-review

15 Citations (Scopus)

Abstract

We prove the global-in-time Strichartz estimates for wave equations on the nontrapping asymptotically conic manifolds. We obtain estimates for the full set of wave admissible indices, including the endpoint. The key points are the properties of the microlocalized spectral measure of Laplacian on this setting showed in [18] and a Littlewood-Paley squarefunction estimate. As applications, we prove the global existence and scattering for a family of nonlinear wave equations on this setting.

Original language	English
Pages (from-to)	91-111
Number of pages	21
Journal	Advances in Mathematics
Volume	271
DOIs	https://doi.org/10.1016/j.aim.2014.11.013
Publication status	Published - 5 Feb 2015

Keywords

Asymptotically conic manifold
Global existence
Scattering theory
Spectral measure
Strichartz estimate

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10.1016/j.aim.2014.11.013

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abstract = "We prove the global-in-time Strichartz estimates for wave equations on the nontrapping asymptotically conic manifolds. We obtain estimates for the full set of wave admissible indices, including the endpoint. The key points are the properties of the microlocalized spectral measure of Laplacian on this setting showed in [18] and a Littlewood-Paley squarefunction estimate. As applications, we prove the global existence and scattering for a family of nonlinear wave equations on this setting.",

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AB - We prove the global-in-time Strichartz estimates for wave equations on the nontrapping asymptotically conic manifolds. We obtain estimates for the full set of wave admissible indices, including the endpoint. The key points are the properties of the microlocalized spectral measure of Laplacian on this setting showed in [18] and a Littlewood-Paley squarefunction estimate. As applications, we prove the global existence and scattering for a family of nonlinear wave equations on this setting.

KW - Asymptotically conic manifold

KW - Global existence

KW - Scattering theory

KW - Spectral measure

KW - Strichartz estimate

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SP - 91

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JO - Advances in Mathematics

JF - Advances in Mathematics

ER -

Strichartz estimates and nonlinear wave equation on nontrapping asymptotically conic manifolds

Abstract

Keywords

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