Global solutions to three-dimensional generalized MHD equations with large initial data

  • Fagui Liu
  • Yu-Zhu WangEmail author


We investigate the initial value problem for the three-dimensional generalized incompressible MHD equations. Firstly, global stability result is established by energy method in the Fourier space. Then for a class of large initial data, global solutions are obtained in the critical function space \(\mathcal {X}^{1-2\alpha }\) by global stability result.


Generalized MHD equations Global solutions Stability 

Mathematics Subject Classification

76W05 76D03 



The work is partially supported by the NNSF of China (Grant No. 11871212).


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsNorth China University of Water Resources and Electric PowerZhengzhouChina

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