Local well-posedness of the fifth-order KDV-type equations on the half-line

Márcio Cavalcante, Chulkwang Kwak

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10 Scopus citations


This paper is a continuation of authors’ previous work [6]. We extend the argument [6] to fifth-order KdV-type equations with different nonlinearities, in specific, where the scaling argument does not hold. We establish the X s,b nonlinear estimates for b < 1 2 , which is almost optimal compared to the standard X s,b nonlinear estimates for b > 2 1 [8, 17]. As an immediate conclusion, we prove the local well-posedness of the initial-boundary value problem (IBVP) for fifth-order KdV-type equations on the right half-line and the left half-line.

Original languageEnglish
Pages (from-to)2607-2661
Number of pages55
JournalCommunications on Pure and Applied Analysis
Issue number5
StatePublished - Sep 2019

Bibliographical note

Funding Information:
2000 Mathematics Subject Classification. 35Q53, 35G31. Key words and phrases. Fifth-order KdV-type equations, initial-boundary value problem, local well-posedness. The second author is supported by FONDECYT de Postdoctorado 2017 Proyecto No. 3170067. ∗ Corresponding author.

Publisher Copyright:
© 2019 American Institute of Mathematical Sciences. All rights reserved.


  • Fifth-order KdV-type equations
  • Initial-boundary value problem
  • Local well-posedness


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