Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field
In the first part of this thesis we extend the theory of anisotropic Triebel-Lizorkin spaces to time-periodic functions. In particular, the spatial trace space is determined together with the existence of extension operators. Additionally, some results regarding pointwise multiplication are provided...
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| Format: | Online |
| Langue: | anglais |
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Logos Verlag Berlin
2021
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| Accès en ligne: | ONIX_20210408_9783832551872_89 |
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| _version_ | 1869514696331100160 |
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| author | Möller, Jens-Henning |
| author_browse | Möller, Jens-Henning |
| author_facet | Möller, Jens-Henning |
| author_sort | Möller, Jens-Henning |
| collection | Directory of Open Access Books |
| description | In the first part of this thesis we extend the theory of anisotropic Triebel-Lizorkin spaces to time-periodic functions. In particular, the spatial trace space is determined together with the existence of extension operators. Additionally, some results regarding pointwise multiplication are provided. As a preparation for this theory we prove a transference principle for multipliers with values in the spaces of summable sequences. Secondly, we consider the equations of magnetohydrodynamics with a background magnetic field and time-periodic forcing. Maximal regularity of the time-periodic linear problem is established by applying the results of the first part. The existence of a solution to the non-linear problem is shown for a large class of background magnetic fields via a fixed-point argument. |
| format | Online |
| id | doab-20.500.12854ir-64447 |
| institution | Directory of Open Access Books |
| language | eng |
| publishDate | 2021 |
| publishDateRange | 2021 |
| publishDateSort | 2021 |
| publisher | Logos Verlag Berlin |
| publisherStr | Logos Verlag Berlin |
| record_format | ojs |
| spelling | doab-20.500.12854ir-644472024-04-04T14:41:08Z Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field Möller, Jens-Henning Triebel-Lizorkin spaces Time-periodic MHD equations Transference principle Trace space thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations In the first part of this thesis we extend the theory of anisotropic Triebel-Lizorkin spaces to time-periodic functions. In particular, the spatial trace space is determined together with the existence of extension operators. Additionally, some results regarding pointwise multiplication are provided. As a preparation for this theory we prove a transference principle for multipliers with values in the spaces of summable sequences. Secondly, we consider the equations of magnetohydrodynamics with a background magnetic field and time-periodic forcing. Maximal regularity of the time-periodic linear problem is established by applying the results of the first part. The existence of a solution to the non-linear problem is shown for a large class of background magnetic fields via a fixed-point argument. 2021-04-08T15:35:21Z 2021-04-08T15:35:21Z 2020 book ONIX_20210408_9783832551872_89 9783832551872 https://directory.doabooks.org/handle/20.500.12854/64447 eng image/jpeg Attribution-NonCommercial-NoDerivatives 4.0 International https://www.logos-verlag.de/cgi-bin/engbuchmid?isbn=5187&lng=eng&id= https://www.logos-verlag.de/ebooks/OA/978-3-8325-5187-2.pdf Logos Verlag Berlin Logos Verlag Berlin 10.30819/5187 10.30819/5187 04b263a1-7fba-4491-9eae-1c394ac42fc3 9783832551872 Logos Verlag Berlin 145 Berlin/Germany open access |
| spellingShingle | Triebel-Lizorkin spaces Time-periodic MHD equations Transference principle Trace space thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations Möller, Jens-Henning Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field |
| title | Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field |
| title_full | Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field |
| title_fullStr | Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field |
| title_full_unstemmed | Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field |
| title_short | Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field |
| title_sort | time periodic solutions to the equations of magnetohydrodynamics with background magnetic field |
| topic | Triebel-Lizorkin spaces Time-periodic MHD equations Transference principle Trace space thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations |
| topic_facet | Triebel-Lizorkin spaces Time-periodic MHD equations Transference principle Trace space thema EDItEUR::P Mathematics and Science::PB Mathematics::PBK Calculus and mathematical analysis::PBKJ Differential calculus and equations |
| url | ONIX_20210408_9783832551872_89 |
| work_keys_str_mv | AT mollerjenshenning timeperiodicsolutionstotheequationsofmagnetohydrodynamicswithbackgroundmagneticfield |