The Cauchy problem for the Novikov equation

被引：57
|
作者：
Yan, Wei [1 ]
Li, Yongsheng [2 ]
Zhang, Yimin [3 ]
机构：
[1] Henan Normal Univ, Coll Math & Informat Sci, Xinxiang 453007, Henan, Peoples R China
[2] S China Univ Technol, Dept Math, Guangzhou 510640, Guangdong, Peoples R China
[3] Chinese Acad Sci, Wuhan Inst Phys & Math, Wuhan 430071, Hubei, Peoples R China
来源：
NODEA-NONLINEAR DIFFERENTIAL EQUATIONS AND APPLICATIONS | 2013年 / 20卷 / 03期
关键词：
Cauchy problem; Novikov equation; Blow-up; WATER-WAVES; TRAJECTORIES; BREAKING;
D O I：
10.1007/s00030-012-0202-1
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we consider the Cauchy problem for the Novikov equation. We prove that the Cauchy problem for the Novikov equation is not locally well-posed in the Sobolev spaces with in the sense that its solutions do not depend uniformly continuously on the initial data. Since the Cauchy problem for the Novikov equation is locally well-posed in with s > 3/2 in the sense of Hadamard, our result implies that s = 3/2 is the critical Sobolev index for well-posedness. We also present two blow-up results of strong solution to the Cauchy problem for the Novikov equation in with s > 3/2.
引用
收藏
页码：1157 / 1169
页数：13
相关论文
共 50 条
  • [11] The Cauchy Problem for the Camassa-Holm-Novikov Equation
    Mingxuan Zhu
    Zaihong Jiang
    Acta Mathematica Scientia, 2023, 43 : 736 - 750
  • [12] On the Cauchy Problem for the Two-Component Novikov Equation
    Mi, Yongsheng
    Mu, Chunlai
    Tao, Weian
    ADVANCES IN MATHEMATICAL PHYSICS, 2013, 2013
  • [13] THE CAUCHY PROBLEM FOR THE CAMASSA-HOLM-NOVIKOV EQUATION
    朱铭旋
    姜在红
    ActaMathematicaScientia, 2023, 43 (02) : 736 - 750
  • [14] The Cauchy Problem for the Camassa-Holm-Novikov Equation
    Zhu, Mingxuan
    Jiang, Zaihong
    ACTA MATHEMATICA SCIENTIA, 2023, 43 (02) : 736 - 750
  • [15] On the Cauchy problem for the modified Novikov equation with peakon solutions
    Mi, Yongsheng
    Mu, Chunlai
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 254 (03) : 961 - 982
  • [16] The global weak solutions to the Cauchy problem of the generalized Novikov equation
    Zhao, Yongye
    Li, Yongsheng
    Yan, Wei
    APPLICABLE ANALYSIS, 2015, 94 (07) : 1334 - 1354
  • [17] On the Cauchy problem of a new integrable two-component Novikov equation
    Yongsheng Mi
    Daiwen Huang
    Monatshefte für Mathematik, 2020, 193 : 361 - 381
  • [18] On the Cauchy problem for the new integrable two-component Novikov equation
    Yongsheng Mi
    Chunlai Mu
    Annali di Matematica Pura ed Applicata (1923 -), 2020, 199 : 1091 - 1122
  • [19] On the Cauchy problem of a new integrable two-component Novikov equation
    Mi, Yongsheng
    Huang, Daiwen
    MONATSHEFTE FUR MATHEMATIK, 2020, 193 (02): : 361 - 381
  • [20] On the Cauchy problem for the new integrable two-component Novikov equation
    Mi, Yongsheng
    Mu, Chunlai
    ANNALI DI MATEMATICA PURA ED APPLICATA, 2020, 199 (03) : 1091 - 1122
12345