The initial-boundary value problem for the Kawahara equation on the half-line

Márcio Cavalcante, Chulkwang Kwak

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10 Scopus citations

Abstract

This paper concerns the initial-boundary value problem of the Kawahara equation posed on the right and left half-lines. We prove the local well-posedness in the low regularity Sobolev space. We introduce the Duhamel boundary forcing operator, which is introduced by Colliander and Kenig (Commun Partial Differ Equ 27:2187–2266, 2002) in the context of Airy group operators, to construct solutions on the whole line. We also give the bilinear estimate in Xs,b space for b<12, which is almost sharp compared to IVP of Kawahara equation (Chen et al. in J Anal Math 107:221–238, 2009; Jia and Huo in J Differ Equ 246:2448–2467, 2009).

Original languageEnglish
Article number45
JournalNonlinear Differential Equations and Applications
Volume27
Issue number5
DOIs
StatePublished - 1 Oct 2020

Bibliographical note

Funding Information:
C. Kwak was partially supported by FONDECYT de Postdoctorado 2017 Proyecto No. 3170067 and project France-Chile ECOS-Sud C18E06, and is supported by the Ewha Womans University Research Grant of 2020, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01068768). The authors are grateful to the anonymous referee for careful reading the manuscript.

Funding Information:
C. Kwak was partially supported by FONDECYT de Postdoctorado 2017 Proyecto No. 3170067 and project France-Chile ECOS-Sud C18E06, and is supported by the Ewha Womans University Research Grant of 2020, and the National Research Foundation of Korea (NRF) grant funded by the Korea government (MSIT) (No. 2020R1F1A1A01068768). The authors are grateful to the anonymous referee for careful reading the manuscript.

Publisher Copyright:
© 2020, Springer Nature Switzerland AG.

Keywords

  • Initial-boundary value problem
  • Kawahara equation
  • Local well-posedness

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