Abstract
In 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
Funding source: National Natural Science Foundation of China
Award Identifier / Grant number: 11401258
Funding source: China Postdoctoral Science Foundation
Award Identifier / Grant number: 2015M581689
Funding statement: The author was supported by National Natural Science Foundation of China (grant No. 11401258) and China Postdoctoral Science Foundation (grant No. 2015M581689).
Acknowledgements
This work was done when the author was visiting the Institute of Mathematics for Industry of Kyushu University. He appreciates the hospitality of Prof. Fukumoto. The author would also like to express his deep thanks to the referee and to Prof. Hao Wu for their valuable suggestions.
References
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