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Journal of Mathematical Fluid Mechanics

, Volume 20, Issue 3, pp 1013–1034 | Cite as

Large Time Existence of Special Strong Solutions to MHD Equations in Cylindrical Domains

  • Bernard Nowakowski
  • Gerhard Ströhmer
  • Wojciech M. Zaja̧czkowski
Open Access
Article

Abstract

We investigate the problem of the existence of regular solutions to the three-dimensional MHD equations in cylindrical domains with perfectly conducting boundaries and under the Navier boundary conditions for the velocity field. We show that if the initial and external data do not change too rapidly along the axis of the cylinder, then there exists a unique regular solution for any finite time.

Keywords

Strong solutions MHD equations Large data 

Mathematics Subject Classification

35Q35 76W05 

Notes

Acknowledgements

The research leading to these results has received funding from the People Programme (Marie Curie Actions) of the European Union’s Seventh Framework Programme FP7/2007-2013/ under REA Grant Agreement No. 319012 and from the Funds for International Co-operation under Polish Ministry of Science and Higher Education Grant Agreement No. 2853/7.PR/2013/2.

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

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© The Author(s) 2017

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

  1. 1.Institute of MathematicsPolish Academy of SciencesWarsawPoland
  2. 2.Department of Mathematics, College of Liberal Arts and SciencesThe University of IowaIowa CityUSA
  3. 3.Institute of Mathematics and CryptologyMilitary University of TechnologyWarsawPoland

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