A Class of Large Solutions to the 3D Generalized Hall-MHD Equations

被引：1
作者：
Wu, Xing [1 ]
Tang, Yanbin [2 ]
机构：
[1] Henan Agr Univ, Coll Informat & Management Sci, Zhengzhou 450002, Henan, Peoples R China
[2] Huazhong Univ Sci & Technol, Sch Math & Stat, Wuhan 430074, Hubei, Peoples R China
来源：
ACTA APPLICANDAE MATHEMATICAE | 2020年 / 169卷 / 01期
关键词：
Generalized Hall-MHD equations; Large solutions; DATA GLOBAL EXISTENCE; BLOW-UP CRITERIA; WELL-POSEDNESS; REGULARITY CRITERIA; DECAY;
D O I：
10.1007/s10440-020-00318-w
中图分类号：
O29 [应用数学];
学科分类号：
070104 ;
摘要：
In this paper we derive the global existence of smooth solutions to the 3D generalized Hall-MHD equations for a class of large initial data, whose L8 norms can be arbitrarily large. In addition, we give an example to show that such a large initial value does exist. Our idea is splitting the generalized heat equations from generalized Hall-MHD system to generate a small quantity for large time t.
引用
收藏
页码：681 / 690
页数：10
相关论文
共 21 条
  • [1] KINETIC FOR MULATION AND GLOBAL EXISTENCE FOR THE HALL-MAGNETO-HYDRODYNAMICS SYSTEM
    Acheritogaray, Marion
    Degond, Pierre
    Frouvelle, Amic
    Liu, Jian-Guo
    [J]. KINETIC AND RELATED MODELS, 2011, 4 (04) : 901 - 918
  • [2] Bahouri H, 2011, GRUNDLEHR MATH WISS, V343, P1, DOI 10.1007/978-3-642-16830-7_1
  • [3] Local Well-Posedness for the Hall-MHD Equations with Fractional Magnetic Diffusion
    Chae, Dongho
    Wan, Renhui
    Wu, Jiahong
    [J]. JOURNAL OF MATHEMATICAL FLUID MECHANICS, 2015, 17 (04) : 627 - 638
  • [4] Well-posedness for Hall-magnetohydrodynamics
    Chae, Dongho
    Degond, Pierre
    Liu, Jian-Guo
    [J]. ANNALES DE L INSTITUT HENRI POINCARE-ANALYSE NON LINEAIRE, 2014, 31 (03): : 555 - 565
  • [5] the blow-up criterion and small data global existence for the Hall-magnetohydrodynamics
    Chae, Dongho
    Lee, Jihoon
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2014, 256 (11) : 3835 - 3858
  • [6] On the temporal decay for the Hall-magnetohydrodynamic equations
    Chae, Dongho
    Schonbek, Maria
    [J]. JOURNAL OF DIFFERENTIAL EQUATIONS, 2013, 255 (11) : 3971 - 3982
  • [7] On well-posedness and blow-up for the full compressible Hall-MHD system
    Fan, Jishan
    Ahmad, Bashir
    Hayat, Tasawar
    Zhou, Yong
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 31 : 569 - 579
  • [8] On well-posedness and blowup criteria for the magnetohydrodynamics with the Hall and ion-slip effects
    Fan, Jishan
    Jia, Xuanji
    Nakamura, Gen
    Zhou, Yong
    [J]. ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND PHYSIK, 2015, 66 (04): : 1695 - 1706
  • [9] On regularity criteria for the 3D Hall-MHD equations in terms of the velocity
    He, Fangyi
    Ahmad, Bashir
    Hayat, Tasawar
    Zhou, Yong
    [J]. NONLINEAR ANALYSIS-REAL WORLD APPLICATIONS, 2016, 32 : 35 - 51
  • [10] Existence and uniqueness of the solution to the dissipative 2D quasi-geostrophic equations in the Sobolev space
    Ju, N
    [J]. COMMUNICATIONS IN MATHEMATICAL PHYSICS, 2004, 251 (02) : 365 - 376
123