Geodesic
On global regular solutions to the mhd equations in a smooth toroidal domain
Alexander Mikhaylov 1   ; Joanna Rencławowicz 2   ; Wojciech M. Zajączkowski 3
1 Steklov Institute of Mathematics Fontanka 7 St. Petersburg, Russia
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland
3 Institute 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
Applicationes Mathematicae, Tome 44 (2017) no. 2, pp. 163-183 Cet article a éte moissonné depuis la source Institute of Mathematics Polish Academy of Sciences

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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.
DOI : 10.4064/am2284-2-2017
Keywords: consider magnetohydrodynamic equations smooth toroid located positive distance its axis symmetry since domain axially symmetric prove existence global regular axially symmetric solutions stability these solutions proved existence global regular solutions close axially symmetric solutions time shown

Alexander Mikhaylov  1   ; Joanna Rencławowicz  2   ; Wojciech M. Zajączkowski  3

1 Steklov Institute of Mathematics Fontanka 7 St. Petersburg, Russia
2 Institute of Mathematics Polish Academy of Sciences Śniadeckich 8 00-656 Warszawa, Poland
3 Institute 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 
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     title = {On global regular solutions to the mhd equations in a smooth toroidal domain},
     journal = {Applicationes Mathematicae},
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Alexander Mikhaylov; Joanna Rencławowicz; Wojciech M. Zajączkowski. On global regular solutions to the mhd equations in a smooth toroidal domain. Applicationes Mathematicae, Tome 44 (2017) no. 2, pp. 163-183. doi: 10.4064/am2284-2-2017

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