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

Márcio Cavalcante; Chulkwang Kwak

doi:10.3934/cpaa.2019117

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

Márcio Cavalcante, Chulkwang Kwak

Department of Mathematics

Research output: Contribution to journal › Article › peer-review

10 Scopus citations

Abstract

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 language	English
Pages (from-to)	2607-2661
Number of pages	55
Journal	Communications on Pure and Applied Analysis
Volume	18
Issue number	5
DOIs	https://doi.org/10.3934/cpaa.2019117
State	Published - 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.

Keywords

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

Access to Document

10.3934/cpaa.2019117

Cite this

@article{552fdc23b32d405cba6ea892b2f8cb2f,

title = "Local well-posedness of the fifth-order KDV-type equations on the half-line",

abstract = " This paper is a continuation of authors{\textquoteright} 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.",

keywords = "Fifth-order KdV-type equations, Initial-boundary value problem, Local well-posedness",

author = "M{\'a}rcio Cavalcante and Chulkwang Kwak",

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: {\textcopyright} 2019 American Institute of Mathematical Sciences. All rights reserved.",

year = "2019",

month = sep,

doi = "10.3934/cpaa.2019117",

language = "English",

volume = "18",

pages = "2607--2661",

journal = "Communications on Pure and Applied Analysis",

issn = "1534-0392",

publisher = "American Institute of Mathematical Sciences",

number = "5",

}

TY - JOUR

T1 - Local well-posedness of the fifth-order KDV-type equations on the half-line

AU - Cavalcante, Márcio

AU - Kwak, Chulkwang

N1 - 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.

PY - 2019/9

Y1 - 2019/9

N2 - 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.

AB - 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.

KW - Fifth-order KdV-type equations

KW - Initial-boundary value problem

KW - Local well-posedness

UR - http://www.scopus.com/inward/record.url?scp=85064242837&partnerID=8YFLogxK

U2 - 10.3934/cpaa.2019117

DO - 10.3934/cpaa.2019117

M3 - Article

AN - SCOPUS:85064242837

SN - 1534-0392

VL - 18

SP - 2607

EP - 2661

JO - Communications on Pure and Applied Analysis

JF - Communications on Pure and Applied Analysis

IS - 5

ER -

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

Abstract

Bibliographical note

Keywords

Access to Document

Fingerprint

Cite this