Ill-posedness for the Camassa-Holm and related equations in Besov spaces

被引：32

作者：

Li, Jinlu ^{[1
]}

Yu, Yanghai ^{[2
]}

Zhu, Weipeng ^{[3
]}

机构：

[1] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China

[2] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

[3] Foshan Univ, Sch Math & Big Data, Foshan 528000, Guangdong, Peoples R China

来源：

JOURNAL OF DIFFERENTIAL EQUATIONS | 2022年 / 306卷

基金：

中国国家自然科学基金;

关键词：

Camassa-Holm equation; Shallow water wave models; Ill-posedness; Besov space; SHALLOW-WATER EQUATION; WELL-POSEDNESS; NONUNIFORM DEPENDENCE; CAUCHY-PROBLEM; INITIAL DATA; EXISTENCE; TRAJECTORIES; STABILITY; BREAKING; FAMILY;

D O I：

10.1016/j.jde.2021.10.052

中图分类号：

O1 [数学];

学科分类号：

0701 ; 070101 ;

摘要：

In this paper, we give a construction of u(0) is an element of B-p,infinity(sigma) such that the corresponding solution to the Camassa-Holm equation starting from u(0) is discontinuous at t = 0 in the metric of B-p,infinity(sigma), which implies the ill-posedness for this equation in B-p,infinity(sigma). We also apply our method to the b-equation and Novikov equation. (C) 2021 Published by Elsevier Inc.

引用

页码：403 / 417

页数：15

共 35 条

[1]

Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1

[2] Existence time for the Camassa-Holm equation and the critical Sobolev index [J].

Byers, Peter .

INDIANA UNIVERSITY MATHEMATICS JOURNAL, 2006, 55 (03) :941-954

[3] AN INTEGRABLE SHALLOW-WATER EQUATION WITH PEAKED SOLITONS [J].

CAMASSA, R ;

HOLM, DD .

PHYSICAL REVIEW LETTERS, 1993, 71 (11) :1661-1664

[4]

Constantin A, 2000, COMMUN PUR APPL MATH, V53, P603

[5]

Constantin A, 1998, COMMUN PUR APPL MATH, V51, P475, DOI 10.1002/(SICI)1097-0312(199805)51:5<475::AID-CPA2>3.0.CO

[6]

2-5

[7] Wave breaking for nonlinear nonlocal shallow water equations [J].

Constantin, A ;

Escher, J .

ACTA MATHEMATICA, 1998, 181 (02) :229-243

[8] On the scattering problem for the Camassa-Holm equation [J].

Constantin, A .

PROCEEDINGS OF THE ROYAL SOCIETY A-MATHEMATICAL PHYSICAL AND ENGINEERING SCIENCES, 2001, 457 (2008) :953-970

[9] Existence of permanent and breaking waves for a shallow water equation: A geometric approach [J].

Constantin, A .

ANNALES DE L INSTITUT FOURIER, 2000, 50 (02) :321-+

[10]

Constantin A., 1997, EXPO MATH, V15, P53

← 1 2 3 4 →