Article Dans Une Revue Analysis & PDE Année : 2024

Global well-posedness for a system of quasilinear wave equations on a product space

Résumé

We consider a system of quasilinear wave equations on the product space $\mathbb{R}^{1+3}\times \mathbb{S}^1$, which we want to see as a toy model for Einstein equations with additional compact dimensions. We show global existence 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.

Dates et versions

hal-03851781 , version 1 (14-11-2022)

Identifiants

Citer

Cécile Huneau, Annalaura Stingo. Global well-posedness for a system of quasilinear wave equations on a product space. Analysis & PDE, 2024, 17 (6), pp.2033-2075. ⟨10.2140/apde.2024.17.2033⟩. ⟨hal-03851781⟩
66 Consultations
0 Téléchargements

Altmetric

Partager

  • More