Global existence for systems of quasilinear wave equations in (1 + 4)-dimensions

Jason Metcalfe, Katrina Morgan*

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review

Abstract

Hörmander proved global existence of solutions for sufficiently small initial data for scalar wave equations in (1+4)-dimensions of the form □u=Q(u,u,u) where Q vanishes to second order and (∂u 2Q)(0,0,0)=0. Without the latter condition, only almost global existence may be guaranteed. The first author and Sogge considered the analog exterior to a star-shaped obstacle. Both results relied on writing the lowest order terms u∂αu=1/2∂αu2 and as such do not immediately generalize to systems. The current study remedies such and extends both results to the case of multiple speed systems.

Original languageEnglish (US)
Pages (from-to)2309-2331
Number of pages23
JournalJournal of Differential Equations
Volume268
Issue number5
DOIs
StatePublished - Feb 15 2020

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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