Ill-posedness of the Camassa–Holm and related equations in the critical space

Zihua Guo, Xingxing Liu, Luc Molinet, Zhaoyang Yin

Research output: Contribution to journalArticleResearchpeer-review

22 Citations (Scopus)

Abstract

We prove norm inflation and hence ill-posedness for a class of shallow water wave equations, such as the Camassa–Holm equation, Degasperis–Procesi equation and Novikov equation etc., in the critical Sobolev space H3/2 and even in the Besov space Bp,r 1+1/p for p∈[1,∞],r∈(1,∞]. Our results cover both real-line and torus cases (only real-line case for Novikov), solving an open problem left in the previous works ([5,14,16]).

Original languageEnglish
Pages (from-to)1698-1707
Number of pages10
JournalJournal of Differential Equations
Volume266
Issue number2-3
DOIs
Publication statusPublished - 15 Jan 2019

Keywords

  • Camassa–Holm equation
  • Critical space
  • Ill-posedness
  • Norm inflation
  • Shallow water wave models

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