数学物理学报(英文版) ›› 2019, Vol. 39 ›› Issue (2): 469-490.doi: 10.1007/s10473-019-0212-8

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GLOBAL EXISTENCE AND OPTIMAL CONVERGENCE RATES OF SOLUTIONS FOR THREE-DIMENSIONAL ELECTROMAGNETIC FLUID SYSTEM

李银1, 位瑞英1, 姚正安2   

  1. 1. School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China;
    2. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • 收稿日期:2018-01-26 修回日期:2018-07-15 出版日期:2019-04-25 发布日期:2019-05-06
  • 通讯作者: Ruiying WEI E-mail:weiruiying521@163.com
  • 作者简介:Yin LI,liyin2009521@163.com;Zheng-an YAO,mcsyao@mail.sysu.edu.cn
  • 基金资助:
    This work is partially supported by the National Natural Science Foundation of China (11501373, 11701380, 11271381), Guangdong Provincial Culture of Seedling of China (2013LYM0081), the Natural Science Foundation of Guangdong Province (2017A030307022, 2016A0300310019, 2016A030307042), the Education Research Platform Project of Guangdong Province (2014KQNCX208), the Education Reform Project of Guangdong Province (2015558).

GLOBAL EXISTENCE AND OPTIMAL CONVERGENCE RATES OF SOLUTIONS FOR THREE-DIMENSIONAL ELECTROMAGNETIC FLUID SYSTEM

Yin LI1, Ruiying WEI1, Zheng-an YAO2   

  1. 1. School of Mathematics and Statistics, Shaoguan University, Shaoguan 512005, China;
    2. Department of Mathematics, Sun Yat-sen University, Guangzhou 510275, China
  • Received:2018-01-26 Revised:2018-07-15 Online:2019-04-25 Published:2019-05-06
  • Contact: Ruiying WEI E-mail:weiruiying521@163.com
  • Supported by:
    This work is partially supported by the National Natural Science Foundation of China (11501373, 11701380, 11271381), Guangdong Provincial Culture of Seedling of China (2013LYM0081), the Natural Science Foundation of Guangdong Province (2017A030307022, 2016A0300310019, 2016A030307042), the Education Research Platform Project of Guangdong Province (2014KQNCX208), the Education Reform Project of Guangdong Province (2015558).

摘要: In this article, we study the electromagnetic fluid system in three-dimensional whole space R3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the Lp - Lq estimates for the linearized equations and an elaborate energy method when the L1-norm of the perturbation is bounded.

关键词: electromagnetic fluid, decay rates, Fourier-splitting method

Abstract: In this article, we study the electromagnetic fluid system in three-dimensional whole space R3. Under assumption of small initial data, we establish the unique global solution by energy method. Moreover, we obtain the time decay rates of the higher-order spatial derivatives of the solution by combining the Lp - Lq estimates for the linearized equations and an elaborate energy method when the L1-norm of the perturbation is bounded.

Key words: electromagnetic fluid, decay rates, Fourier-splitting method