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Long time behavior of solutions to 3D generalized MHD equations

  • Xiaopeng Zhao EMAIL logo
From the journal Forum Mathematicum


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 3, we establish the sharp algebraic decay rate of solutions to the generalized MHD system provided that the parameters satisfy α,β(0,2].

MSC 2010: 35B40; 35Q35; 76W05

Communicated by Christopher D. Sogge

Award Identifier / Grant number: 11401258

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).


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.


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Received: 2019-06-19
Revised: 2019-10-24
Published Online: 2020-04-15
Published in Print: 2020-07-01

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