The Fuchsian approach to global existence for hyperbolic equations

Florian Beyer, Todd A. Oliynyk, J. Arturo Olvera-Santamaría

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5 Citations (Scopus)

Abstract

We analyze the Cauchy problem for symmetric hyperbolic equations with a time singularity of Fuchsian type and establish a global existence theory along with decay estimates for evolutions toward the singular time under a small initial data assumption. We, then, apply this theory to semilinear wave equations near spatial infinity on Minkowski and Schwarzschild spacetimes, and to the relativistic Euler equations with Gowdy symmetry on Kasner spacetimes.

Original languageEnglish
Pages (from-to)864-934
Number of pages71
JournalCommunications in Partial Differential Equations
Volume46
Issue number5
DOIs
Publication statusPublished - 2021

Keywords

  • Decay estimates
  • Fuchsian equations
  • global existence
  • non-linear wave equations
  • null condition
  • system of hyperbolic equations

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