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

Jens-Henning Möller

ISBN 978-3-8325-5187-2
145 pages, year of publication: 2020
price: 37.50 €
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.

Table of contents (PDF)

Keywords:

  • Triebel-Lizorkin spaces
  • Time-periodic
  • MHD equations
  • Transference principle
  • Trace space

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