A remark on norm inflation for nonlinear wave equations

Justin Forlano, Mamoru Okamoto

Research output: Contribution to journalArticlepeer-review

Abstract

In this note, we study the ill-posedness of nonlinear wave equations (NLW). Namely, we show that NLW experiences norm inflation at every initial data in negative Sobolev spaces. This result covers a gap left open in a paper of Christ, Colliander, and Tao (2003) and extends the result by Oh, Tzvetkov, and the second author (2019) to non-cubic integer nonlinearities. In particular, for some low dimensional cases, we obtain norm inflation above the scaling critical regularity. We also prove ill-posedness for NLW, via norm inflation at general initial data, in negative regularity Fourier-Lebesgue and Fourier-amalgam spaces.

Original languageEnglish
Pages (from-to)361-381
Number of pages21
JournalDynamics of Partial Differential Equations
Volume17
Issue number4
DOIs
Publication statusPublished - Dec 2020

Keywords

  • Ill-posedness
  • nonlinear wave equation
  • Norm inflation

ASJC Scopus subject areas

  • Analysis
  • Applied Mathematics

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