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Global Classical Solutions of Three Dimensional Viscous MHD System Without Magnetic Diffusion on Periodic Boxes

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Abstract

In this paper, we study the global existence of classical solutions to the three dimensional incompressible viscous magneto-hydrodynamical system without magnetic diffusion on periodic boxes, that is, with periodic boundary conditions. We work in Eulerian coordinates and employ a time-weighted energy estimate to prove the global existence result, under the assumptions that the initial magnetic field is close enough to an equilibrium state and the initial data have some symmetries.

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Authors and Affiliations

  1. School of Mathematics, Georgia Institute of Technology, Atlanta, GA, 30332, USA

    Ronghua Pan

  2. School of Mathematical Sciences, Fudan University, Shanghai, 200433, People’s Republic of China

    Yi Zhou

  3. Department of Mathematics, East China University of Science and Technology, Shanghai, 200237, People’s Republic of China

    Yi Zhu

Authors
  1. Ronghua Pan
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  2. Yi Zhou
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  3. Yi Zhu
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Correspondence to Yi Zhu.

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Communicated by F. Lin

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Pan, R., Zhou, Y. & Zhu, Y. Global Classical Solutions of Three Dimensional Viscous MHD System Without Magnetic Diffusion on Periodic Boxes. Arch Rational Mech Anal 227, 637–662 (2018). https://doi.org/10.1007/s00205-017-1170-8

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  • DOI: https://doi.org/10.1007/s00205-017-1170-8

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