On global regular solutions to magnetohydrodynamics in axi-symmetric domains

Open Access


We consider mhd equations in three-dimensional axially symmetric domains under the Navier boundary conditions for both velocity and magnetic fields. We prove the existence of global, regular axi-symmetric solutions and examine their stability in the class of general solutions to the mhd system. As a consequence, we show the existence of global, regular solutions to the mhd system which are close in suitable norms to axi-symmetric solutions.


Magnetohydrodynamics Stability of axially symmetric solutions Global existence of regular solutions 

Mathematics Subject Classification

35Q35 76D03 76W05 


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© The Author(s) 2016

Open AccessThis article is distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution, and reproduction in any medium, provided you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons license, and indicate if changes were made.

Authors and Affiliations

  • Bernard Nowakowski
    • 1
  • Wojciech M. Zajączkowski
    • 1
    • 2
  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland
  2. 2.Cybernetics Faculty, Institute of Mathematics and CryptologyMilitary University of TechnologyWarsawPoland

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