On global regular solutions to the mhd equations in a smooth toroidal domain

Volume 44 / 2017

Alexander Mikhaylov, Joanna Rencławowicz, Wojciech M. Zajączkowski Applicationes Mathematicae 44 (2017), 163-183 MSC: 35B07, 35B35, 35B40, 76W05. DOI: 10.4064/am2284-2-2017 Published online: 8 June 2017

Abstract

We consider the magnetohydrodynamic equations in a smooth toroid located at a positive distance from its axis of symmetry. Since the domain is axially symmetric, we can prove existence of global regular axially symmetric solutions. Next, stability of these solutions is proved. In this way the existence of global regular solutions close to the axially symmetric solutions for all time is shown.

Authors

  • Alexander MikhaylovSteklov Institute of Mathematics
    Fontanka 7
    St. Petersburg, Russia
  • Joanna RencławowiczInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    e-mail
  • Wojciech M. ZajączkowskiInstitute of Mathematics
    Polish Academy of Sciences
    Śniadeckich 8
    00-656 Warszawa, Poland
    and
    Institute of Mathematics and Cryptology
    Cybernetics Faculty
    Military University of Technology
    Kaliskiego 2
    00-908 Warszawa, Poland
    e-mail

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