Regularity Criteria for the Viscous Camassa-Holm Equations

被引：19
|
作者：
Zhou, Yong [1 ]
Fan, Jishan [2 ]
机构：
[1] Zhejiang Normal Univ, Dept Math, Jinhua 321004, Zhejiang, Peoples R China
[2] Nanjing Forestry Univ, Dept Appl Math, Nanjing 210037, Jiangsu, Peoples R China
来源：
INTERNATIONAL MATHEMATICS RESEARCH NOTICES | 2009年 / 2009卷 / 13期
关键词：
NAVIER-STOKES EQUATIONS; WEAK SOLUTIONS; PRESSURE; TERMS;
D O I：
10.1093/imrn/rnp023
中图分类号：
O1 [数学];
学科分类号：
0701 ; 070101 ;
摘要：
In this paper, we consider the viscous n-dimensional Camassa-Holm equations in the whole space. Various regularity criteria for the strong solution are established. As a corollary, we show the existence of a global smooth solution when n <= 4.
引用
收藏
页码：2508 / 2518
页数：11
相关论文
共 50 条
  • [21] Gevrey regularity and analyticity for the modified Camassa-Holm equation
    Zhou, Qingyu
    Pan, Xiaolin
    Zhou, Shouming
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2022, 29 (03) : 493 - 503
  • [22] An optimal control problem of the 3D viscous Camassa-Holm equations
    Cung The Anh
    Dang Thanh Son
    OPTIMIZATION, 2021, 70 (01) : 3 - 25
  • [23] Gevrey regularity and analyticity for Camassa-Holm type systems
    Luo, Wei
    Yin, Zhaoyang
    ANNALI DELLA SCUOLA NORMALE SUPERIORE DI PISA-CLASSE DI SCIENZE, 2018, 18 (03) : 1061 - 1079
  • [24] Lower order regularity for the generalized Camassa-Holm equation
    Mi, Yongsheng
    Guo, Boling
    Mu, Chunlai
    APPLICABLE ANALYSIS, 2017, 96 (07) : 1126 - 1137
  • [25] OPTIMAL SOLUTION FOR THE VISCOUS MODIFIED CAMASSA-HOLM EQUATION
    Gao, Anna
    Shen, Chunyu
    JOURNAL OF NONLINEAR MATHEMATICAL PHYSICS, 2010, 17 (04) : 571 - 589
  • [26] THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS
    杨灵娥
    纪艳珊
    郭柏灵
    Acta Mathematica Scientia, 2009, 29 (01) : 65 - 73
  • [27] THE RELATION OF TWO-DIMENSIONAL VISCOUS CAMASSA-HOLM EQUATIONS AND THE NAVIER-STOKES EQUATIONS
    Yang Linge
    Ji Yanshan
    Guo Boling
    ACTA MATHEMATICA SCIENTIA, 2009, 29 (01) : 65 - 73
  • [28] Local null controllability of viscous Camassa-Holm equation
    Mitra, Debanjana
    JOURNAL OF EVOLUTION EQUATIONS, 2018, 18 (02) : 627 - 657
  • [29] On the Camassa-Holm and Hunter-Saxton equations
    Holden, H
    European Congress of Mathematics, 2005, : 173 - 200
  • [30] Derivation of the Camassa-Holm equations for elastic waves
    Erbay, H. A.
    Erbay, S.
    Erkip, A.
    PHYSICS LETTERS A, 2015, 379 (12-13) : 956 - 961
12345