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
  • [31] On the Camassa-Holm and Hunter-Saxton equations
    Holden, H
    European Congress of Mathematics, 2005, : 173 - 200
  • [32] Time periodic solution of the viscous Camassa-Holm equation
    Fu, YP
    Guo, BL
    JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 2006, 313 (01) : 311 - 321
  • [33] Nonlocal Symmetries of the Camassa-Holm Type Equations
    Lu Zhao
    Changzheng Qu
    Chinese Annals of Mathematics, Series B, 2020, 41 : 407 - 418
  • [34] The Pullback Attractors for the Nonautonomous Camassa-Holm Equations
    Wu, Delin
    MATHEMATICAL PROBLEMS IN ENGINEERING, 2009, 2009
  • [35] EMBEDDING CAMASSA-HOLM EQUATIONS IN INCOMPRESSIBLE EULER
    Natale, Andrea
    Vialard, Francois-Xavier
    JOURNAL OF GEOMETRIC MECHANICS, 2019, 11 (02): : 205 - 223
  • [36] Optimal control of the viscous generalized Camassa-Holm equation
    Shen, Chunyu
    Gao, Anna
    Tian, Lixin
    NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2010, 11 (03) : 1835 - 1846
  • [37] Regularity and stability of finite energy weak solutions for the Camassa-Holm equations with nonlocal viscosity
    Gan, Zaihui
    Guo, Qing
    Lu, Yong
    CALCULUS OF VARIATIONS AND PARTIAL DIFFERENTIAL EQUATIONS, 2021, 60 (01)
  • [38] Numerical study of fractional Camassa-Holm equations
    Klein, Christian
    Oruc, Goksu
    PHYSICA D-NONLINEAR PHENOMENA, 2024, 457
  • [39] Improved blow-up criteria for some Camassa-Holm type equations
    Zheng, Rudong
    JOURNAL OF DIFFERENTIAL EQUATIONS, 2025, 415 : 182 - 201
  • [40] Nonlocal Symmetries of the Camassa-Holm Type Equations
    Zhao, Lu
    Qu, Changzheng
    CHINESE ANNALS OF MATHEMATICS SERIES B, 2020, 41 (03) : 407 - 418
12345