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

doi:10.1007/s10473-019-0212-8

Acta mathematica scientia,Series B ›› 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

Yin LI¹, Ruiying WEI¹, Zheng-an YAO²

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).

Abstract

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 L^p - L^q 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

Yin LI, Ruiying WEI, Zheng-an YAO. GLOBAL EXISTENCE AND OPTIMAL CONVERGENCE RATES OF SOLUTIONS FOR THREE-DIMENSIONAL ELECTROMAGNETIC FLUID SYSTEM[J].Acta mathematica scientia,Series B, 2019, 39(2): 469-490.

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

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