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oapen-20.500.12657-567872023-02-01T09:02:24Z Existence and Spatial Decay of Periodic Navier–Stokes Flows in Exterior Domains Eiter, Thomas A classical problem in the field of mathematical fluid mechanics is the flow of a viscous incompressible fluid past a rigid body. In his doctoral thesis, Thomas Walter Eiter investigates time-periodic solutions to the associated Navier-Stokes equations when the body performs a non-trivial translation. The first part of the thesis is concerned with the question of existence of time-periodic solutions in the case of a non-rotating and of a rotating obstacle. Based on an investigation of the corresponding Oseen linearizations, new existence results in suitable function spaces are established. The second part deals with the study of spatially asymptotic properties of time-periodic solutions. For this purpose, time-periodic fundamental solutions to the Stokes and Oseen linearizations are introduced and investigated, and the concept of a time-periodic fundamental solution for the vorticity field is developed. With these results, new pointwise estimates of the velocity and the vorticity field associated to a time-periodic fluid flow are derived. 2022-06-18T05:37:43Z 2022-06-18T05:37:43Z 2020 book 9783832551087 https://library.oapen.org/handle/20.500.12657/56787 eng application/pdf n/a external_content.pdf Logos Verlag Berlin Logos Verlag Berlin https://doi.org/10.30819/5108 https://doi.org/10.30819/5108 1059eef5-b798-421c-b07f-c6a304d3aec8 b818ba9d-2dd9-4fd7-a364-7f305aef7ee9 9783832551087 Knowledge Unlatched (KU) Logos Verlag Berlin Knowledge Unlatched open access
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A classical problem in the field of mathematical fluid mechanics is the flow of a viscous incompressible fluid past a rigid body. In his doctoral thesis, Thomas Walter Eiter investigates time-periodic solutions to the associated Navier-Stokes equations when the body performs a non-trivial translation. The first part of the thesis is concerned with the question of existence of time-periodic solutions in the case of a non-rotating and of a rotating obstacle. Based on an investigation of the corresponding Oseen linearizations, new existence results in suitable function spaces are established.
The second part deals with the study of spatially asymptotic properties of time-periodic solutions. For this purpose, time-periodic fundamental solutions to the Stokes and Oseen linearizations are introduced and investigated, and the concept of a time-periodic fundamental solution for the vorticity field is developed. With these results, new pointwise estimates of the velocity and the vorticity field associated to a time-periodic fluid flow are derived.
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