MHD Equations in a Bounded Domain

Maria B. Kania

doi:10.2478/amsil-2021-0008

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MHD Equations in a Bounded Domain

Annales Mathematicae Silesianae

Volume 35 (2021): Issue 2 (September 2021)

By: Maria B. Kania

Open Access

|Jul 2021

Abstract

We consider the MHD system in a bounded domain Ω ⊂ ℝ^N, 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.

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Articles in this issue

DOI: https://doi.org/10.2478/amsil-2021-0008 | Journal eISSN: 2391-4238 | Journal ISSN: 0860-2107

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Language: English

Page range: 211 - 235

Submitted on: Mar 31, 2021

Accepted on: Jul 8, 2021

Published on: Jul 27, 2021

Published by: University of Silesia in Katowice, Institute of Mathematics

In partnership with: Paradigm Publishing Services

Publication frequency: 2 issues per year

Keywords:

MHD equations,

abstract parabolic problem,

fractional approximations

Related subjects:

Mathematics,

General mathematics

© 2021 Maria B. Kania, published by University of Silesia in Katowice, Institute of Mathematics
This work is licensed under the Creative Commons Attribution 4.0 License.

Volume 35 (2021): Issue 2 (September 2021)