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Global well-posedness
for a system of quasilinear wave equations on a product
space
Cécile Huneau and Annalaura Stingo |
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Vol. 17 (2024), No. 6, 2033–2075
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Abstract |
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We consider a system of quasilinear wave equations on the product space , 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. |
Keywords
Kaluza–Klein, general relativity, wave equations
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Mathematical Subject Classification
Primary: 35Q75
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Milestones
Received: 4 November 2021
Revised: 6 September 2022
Accepted: 17 January 2023
Published: 19 July 2024
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Authors |
| Cécile Huneau | |
| École Polytechnique and CNRS Palaiseau France |
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| Annalaura Stingo | |
| École Polytechnique Palaiseau France |
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| © 2024 MSP (Mathematical Sciences Publishers). Distributed under the Creative Commons Attribution License 4.0 (CC BY). |
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