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

被引：3

作者：

Chu, Jixun ^{[1
]}

Coron, Jean-Michel ^{[2
,3
]}

Shang, Peipei ^{[2
,4
,5
]}

Tang, Shu-Xia ^{[2
,6
]}

机构：

[1] Univ Sci & Technol Beijing, Sch Math & Phys, Dept Appl Math, Beijing 100083, Peoples R China

[2] UPMC Univ Paris 06, Sorbonne Univ, Lab Jacques Louis Lions, UMR 7598, 4 Pl Jussieu, F-75252 Paris, France

[3] ETH, ITS, Clausiusstr 47, CH-8092 Zurich, Switzerland

[4] Tongji Univ, Sch Math Sci, Shanghai 200092, Peoples R China

[5] ETH, Inst Math Res ETH FIM, Ramistr 101, CH-8092 Zurich, Switzerland

[6] Univ Waterloo, Dept Appl Math, Waterloo, ON N2L 3G1, Canada

来源：

CHINESE ANNALS OF MATHEMATICS SERIES B | 2018年 / 39卷 / 02期

基金：

中国国家自然科学基金;

关键词：

Korteweg-de Vries equation; Resolvent estimation; Analytic semigroup; Gevrey class; STABILIZATION;

D O I：

10.1007/s11401-018-1060-x

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, the authors consider the Gevrey class regularity of a semigroup associated with a nonlinear Korteweg-dc 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 delta is an element of(3/2, infinity) for t > 0.

引用

页码：201 / 212

页数：12

共 50 条

[1] Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation
Jixun CHU
Jean-Michel CORON
Peipei SHANG
Shu-Xia TANG
Chinese Annals of Mathematics,Series B, 2018, (02) : 201 - 212
[2] Gevrey Class Regularity of a Semigroup Associated with a Nonlinear Korteweg-de Vries Equation
Jixun Chu
Jean-Michel Coron
Peipei Shang
Shu-Xia Tang
Chinese Annals of Mathematics, Series B, 2018, 39 : 201 - 212
[3] On the Generalized Nonlinear Korteweg-De Vries Equation
Gladkov, S. O.
TECHNICAL PHYSICS, 2024, : 2336 - 2338
[4] Gevrey regularizing effect for the (generalized) Korteweg-de Vries equation and nonlinear Schrödinger equations
C.N.R.S., Université de Paris-Sud, Mathématique, Bâtiment 425, Orsay
91405, France
不详
376, Japan
不详
560, Japan
Anna Inst Henri Poincare Anal. Non Lineaire, 6 (673-725):
[5] GEVREY REGULARIZING EFFECT FOR THE (GENERALIZED) KORTEWEG-DE VRIES EQUATION AND NONLINEAR SCHRODINGER-EQUATIONS
DEBOUARD, A
HAYASHI, N
KATO, K
ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 1995, 12 (06): : 673 - 725
[6] On the propagation of regularity for solutions of the fractional Korteweg-de Vries equation
Mendez, Argenis J.
JOURNAL OF DIFFERENTIAL EQUATIONS, 2020, 269 (11) : 9051 - 9089
[7] On the low regularity of the Korteweg-de Vries-Burgers equation
Molinet, L
Ribaud, F
INTERNATIONAL MATHEMATICS RESEARCH NOTICES, 2002, 2002 (37) : 1979 - 2005
[8] KORTEWEG-DE VRIES EQUATION
SHABAT, AB
DOKLADY AKADEMII NAUK SSSR, 1973, 211 (06): : 1310 - 1313
[9] On a class of singular solutions to the Korteweg-de Vries equation
S. I. Pohozaev
Doklady Mathematics, 2010, 82 : 936 - 938
[10] KORTEWEG-DE VRIES EQUATION
TSUTSUMI, M
PROCEEDINGS OF THE JAPAN ACADEMY, 1975, 51 (06): : 399 - 401

← 1 2 3 4 5 →