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Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field
Paperback

Time-Periodic Solutions to the Equations of Magnetohydrodynamics with Background Magnetic Field

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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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MORE INFO
Format
Paperback
Publisher
Logos Verlag Berlin GmbH
Country
Germany
Date
29 October 2020
Pages
145
ISBN
9783832551872

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.

Read More
Format
Paperback
Publisher
Logos Verlag Berlin GmbH
Country
Germany
Date
29 October 2020
Pages
145
ISBN
9783832551872