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 -