Affiliation:
1. School of Sciences, Northeastern University, Shenyang110819; and School of Science, Jiangnan University, Wuxi 214122, P. R. China
Abstract
AbstractIn this paper, we consider the long time behavior of solutions for 3D incompressible MHD equations with fractional Laplacian.
Firstly, in a periodic bounded domain, we prove the existence of a global attractor. The analysis reveals a relation between the Laplacian exponent and the regularity of the spaces of velocity and magnetic fields. Finally, in the whole space {\mathbb{R}^{3}}, we establish the sharp algebraic decay rate of solutions to the generalized MHD system provided that the parameters satisfy {\alpha,\beta\in(0,2]}.
Funder
National Natural Science Foundation of China
China Postdoctoral Science Foundation
Subject
Applied Mathematics,General Mathematics
Reference80 articles.
1. Analysis and approximation of a fractional Cahn–Hilliard equation;SIAM J. Numer. Anal.,2017
2. BKM’s criterion and global weak solutions for magnetohydrodynamics with zero viscosity;Discrete Contin. Dyn. Syst.,2009
3. Regularity criteria for the generalized MHD equations;Comm. Partial Differential Equations,2008
4. On the global well-posedness of N-dimensional generalized MHD system in anisotropic spaces;Adv. Differential Equations,2014
Cited by
2 articles.
订阅此论文施引文献
订阅此论文施引文献，注册后可以免费订阅5篇论文的施引文献，订阅后可以查看论文全部施引文献