Global well-posedness for 2D nonlinear wave equations without compact support

Yuan Cai, Zhen Lei, Nader Masmoudi

Research output: Contribution to journalArticle

Abstract

In the significant work of [6], Alinhac proved the global existence of small solutions for 2D quasilinear wave equations under the null conditions. The proof heavily relies on the fact that the initial data have compact support [23]. Whether this constraint can be removed or not is still unclear. In this paper, for fully nonlinear wave equations under the null conditions, we prove the global well-posedness for small initial data without compact support. Moreover, we apply our result to a class of quasilinear wave equations.

Original languageEnglish (US)
Pages (from-to)211-234
Number of pages24
JournalJournal des Mathematiques Pures et Appliquees
Volume114
DOIs
StatePublished - Jun 2018

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Keywords

  • Global well-posedness
  • Null condition
  • Two dimensional nonlinear wave equations
  • Without compact support

ASJC Scopus subject areas

  • Mathematics(all)
  • Applied Mathematics

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