Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

Jixun Chu; Jean Michel Coron; Peipei Shang; Shu Xia Tang

doi:10.1007/s11401-018-1060-x

Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

Jixun Chu, Jean Michel Coron, Peipei Shang, Shu Xia Tang

Mechanical Engineering

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

2 Scopus citations

Abstract

In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class δ ∈ (3/2, ∞) for t > 0.

Original language	English
Pages (from-to)	201-212
Number of pages	12
Journal	Chinese Annals of Mathematics. Series B
Volume	39
Issue number	2
DOIs	https://doi.org/10.1007/s11401-018-1060-x
State	Published - Mar 1 2018

Keywords

Analytic semigroup
Gevrey class
Korteweg-de Vries equation
Resolvent estimation

Access to Document

10.1007/s11401-018-1060-x

Cite this

@article{3da79484b3f24cd9a9684b8cd062dc3d,

title = "Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation",

abstract = "In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class δ ∈ (3/2, ∞) for t > 0.",

keywords = "Analytic semigroup, Gevrey class, Korteweg-de Vries equation, Resolvent estimation",

author = "Jixun Chu and Coron, {Jean Michel} and Peipei Shang and Tang, {Shu Xia}",

note = "Publisher Copyright: {\textcopyright} 2018, Fudan University and Springer-Verlag GmbH Germany, part of Springer Nature.",

year = "2018",

month = mar,

day = "1",

doi = "10.1007/s11401-018-1060-x",

language = "English",

volume = "39",

pages = "201--212",

journal = "Chinese Annals of Mathematics. Series B",

issn = "0252-9599",

number = "2",

}

TY - JOUR

T1 - Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

AU - Chu, Jixun

AU - Coron, Jean Michel

AU - Shang, Peipei

AU - Tang, Shu Xia

PY - 2018/3/1

Y1 - 2018/3/1

N2 - In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class δ ∈ (3/2, ∞) for t > 0.

AB - In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-de Vries (KdV for short) equation. By estimating the resolvent of the corresponding linear operator, the authors conclude that the semigroup generated by the linear operator is not analytic but of Gevrey class δ ∈ (3/2, ∞) for t > 0.

KW - Analytic semigroup

KW - Gevrey class

KW - Korteweg-de Vries equation

KW - Resolvent estimation

UR - http://www.scopus.com/inward/record.url?scp=85041733612&partnerID=8YFLogxK

U2 - 10.1007/s11401-018-1060-x

DO - 10.1007/s11401-018-1060-x

M3 - Article

AN - SCOPUS:85041733612

SN - 0252-9599

VL - 39

SP - 201

EP - 212

JO - Chinese Annals of Mathematics. Series B

JF - Chinese Annals of Mathematics. Series B

IS - 2

ER -

Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation

Abstract

Keywords

Access to Document

Other files and links

Fingerprint

Cite this