<abstract xmlns="http://www.w3.org/1999/xhtml">We consider the MHD system in a bounded domain Ω ⊂ ℝ<italic>N</italic>, <italic>N</italic> = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa estimates we construct global in time, unique solutions to fractional approximations of the MHD system in the base space (<italic>L</italic>2(Ω
))<italic>N</italic> × (<italic>L</italic>2(Ω
))<italic>N</italic>. Solutions to MHD system are obtained next as a limits of that fractional approximations.</abstract>

We consider the MHD system in a bounded domain Ω ⊂ ℝN, N = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa estimates we construct global in time, unique solutions to fractional approximations of the MHD system in the base space (L2(Ω
))N × (L2(Ω
))N. Solutions to MHD system are obtained next as a limits of that fractional approximations.

MHD Equations in a Bounded Domain

Annales Mathematicae Silesianae

This work is licensed under the Creative Commons Attribution 4.0 International License.

{"article-title":"MHD Equations in a Bounded Domain"}

We consider the MHD system in a bounded domain Ω ⊂ ℝN, N = 2; 3, with Dirichlet boundary conditions. Using Dan Henry’s semigroup approach and Giga–Miyakawa...

MHD Equations in a Bounded Domain

Publié en ligne: 27 juil. 2021

Pages: 211 - 235

Reçu: 31 mars 2021

Accepté: 08 juil. 2021

DOI: https://doi.org/10.2478/amsil-2021-0008

Mots clés
MHD equations, abstract parabolic problem, fractional approximations

© 2021 Maria B. Kania, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

MHD Equations in a Bounded Domain

Publié en ligne: 27 juil. 2021

Pages: 211 - 235

Reçu: 31 mars 2021

Accepté: 08 juil. 2021

DOI: https://doi.org/10.2478/amsil-2021-0008

Mots clésMHD equations, abstract parabolic problem, fractional approximations

© 2021 Maria B. Kania, published by Sciendo

This work is licensed under the Creative Commons Attribution 4.0 International License.

Mots clés
MHD equations, abstract parabolic problem, fractional approximations