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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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Logos Verlag Berlin
2022
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oapen-20.500.12657-568102023-02-01T08:50:22Z Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field Möller, Jens-Henning Technology & Engineering Agriculture bic Book Industry Communication::T Technology, engineering, agriculture::TV Agriculture & farming 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. 2022-06-18T05:40:01Z 2022-06-18T05:40:01Z 2020 book 9783832551872 https://library.oapen.org/handle/20.500.12657/56810 eng application/pdf n/a external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/5187 https://doi.org/10.30819/5187 1059eef5-b798-421c-b07f-c6a304d3aec8 b818ba9d-2dd9-4fd7-a364-7f305aef7ee9 9783832551872 Knowledge Unlatched (KU) Logos Verlag Berlin Knowledge Unlatched open access |
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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. |
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2022 |
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