GLOBAL WELL-POSEDNESS FOR A SYSTEM OF QUASILINEAR WAVE EQUATIONS ON A PRODUCT SPACE

Cécile Huneau; Annalaura Stingo

doi:10.2140/apde.2024.17.2033

GLOBAL WELL-POSEDNESS FOR A SYSTEM OF QUASILINEAR WAVE EQUATIONS ON A PRODUCT SPACE

Cécile Huneau
, Annalaura Stingo

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

Abstract

We consider a system of quasilinear wave equations on the product space R¹⁺³ ×S¹, which we want to see as a toy model for the Einstein equations with additional compact dimensions. We show global existence of solutions for small and regular initial data with polynomial decay at infinity. The method combines energy estimates on hyperboloids inside the light cone and weighted energy estimates outside the light cone.

Original language	English
Pages (from-to)	2033-2075
Number of pages	43
Journal	Analysis and PDE
Volume	17
Issue number	6
DOIs	https://doi.org/10.2140/apde.2024.17.2033
Publication status	Published - 1 Jan 2024

Keywords

Kaluza–Klein
general relativity
wave equations

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10.2140/apde.2024.17.2033

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abstract = "We consider a system of quasilinear wave equations on the product space R1+3 ×S1, which we want to see as a toy model for the Einstein equations with additional compact dimensions. We show global existence of solutions for small and regular initial data with polynomial decay at infinity. The method combines energy estimates on hyperboloids inside the light cone and weighted energy estimates outside the light cone.",

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author = "C{\'e}cile Huneau and Annalaura Stingo",

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PY - 2024/1/1

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N2 - We consider a system of quasilinear wave equations on the product space R1+3 ×S1, which we want to see as a toy model for the Einstein equations with additional compact dimensions. We show global existence of solutions for small and regular initial data with polynomial decay at infinity. The method combines energy estimates on hyperboloids inside the light cone and weighted energy estimates outside the light cone.

AB - We consider a system of quasilinear wave equations on the product space R1+3 ×S1, which we want to see as a toy model for the Einstein equations with additional compact dimensions. We show global existence of solutions for small and regular initial data with polynomial decay at infinity. The method combines energy estimates on hyperboloids inside the light cone and weighted energy estimates outside the light cone.

KW - Kaluza–Klein

KW - general relativity

KW - wave equations

UR - https://www.scopus.com/pages/publications/85200467851

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DO - 10.2140/apde.2024.17.2033

M3 - Article

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SN - 2157-5045

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JO - Analysis and PDE

JF - Analysis and PDE

IS - 6

ER -

GLOBAL WELL-POSEDNESS FOR A SYSTEM OF QUASILINEAR WAVE EQUATIONS ON A PRODUCT SPACE

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Keywords

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