Kyed, Mads (2012)
Time-Periodic Solutions to the Navier-Stokes Equations.
Technische Universität Darmstadt
Habilitation, Bibliographie
Dies ist die neueste Version dieses Eintrags.
Kurzbeschreibung (Abstract)
The three-dimensional Navier-Stokes system in the whole space with time-periodic data is investigated. Both the case of a vanishing and that of a non-vanishing velocity field at spatial infinity are treated. In the first part of the thesis, a maximal regularity framework for the linearized system is developed in a general L^q-setting. A function space with the property that the corresponding linear operator maps this space homeomorphically onto L^q is identified. Existence of a strong solution herein is then shown for sufficiently "small" data. Moreover, regularity and uniqueness properties are established. In the following part, an asymptotic expansion at spatial infinity of the strong solution is carried out. In particular, the asymptotic profile is completely identified. In the final part, existence of a weak solution is proved without any restriction on the "size" of the data. Furthermore, a decomposition of the weak solution into a time-independent part and a time-periodic part with finite kinetic energy is obtained. On the basis of this decomposition, regularity properties of the weak solution are derived.
| Typ des Eintrags: | Habilitation |
|---|---|
| Erschienen: | 2012 |
| Autor(en): | Kyed, Mads |
| Art des Eintrags: | Bibliographie |
| Titel: | Time-Periodic Solutions to the Navier-Stokes Equations |
| Sprache: | Englisch |
| Publikationsjahr: | 2012 |
| Ort: | Darmstadt |
| Zugehörige Links: | |
| Kurzbeschreibung (Abstract): | The three-dimensional Navier-Stokes system in the whole space with time-periodic data is investigated. Both the case of a vanishing and that of a non-vanishing velocity field at spatial infinity are treated. In the first part of the thesis, a maximal regularity framework for the linearized system is developed in a general L^q-setting. A function space with the property that the corresponding linear operator maps this space homeomorphically onto L^q is identified. Existence of a strong solution herein is then shown for sufficiently "small" data. Moreover, regularity and uniqueness properties are established. In the following part, an asymptotic expansion at spatial infinity of the strong solution is carried out. In particular, the asymptotic profile is completely identified. In the final part, existence of a weak solution is proved without any restriction on the "size" of the data. Furthermore, a decomposition of the weak solution into a time-independent part and a time-periodic part with finite kinetic energy is obtained. On the basis of this decomposition, regularity properties of the weak solution are derived. |
| Freie Schlagworte: | Navier-Stokes, time periodic, maximal regularity, Asymptotic expansion |
| Sachgruppe der Dewey Dezimalklassifikatin (DDC): | 500 Naturwissenschaften und Mathematik > 510 Mathematik |
| Fachbereich(e)/-gebiet(e): | 04 Fachbereich Mathematik 04 Fachbereich Mathematik > Analysis |
| Hinterlegungsdatum: | 16 Feb 2024 07:59 |
| Letzte Änderung: | 16 Feb 2024 07:59 |
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Verfügbare Versionen dieses Eintrags
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Time-Periodic Solutions to the Navier-Stokes Equations. (deposited 18 Mär 2013 16:27)
- Time-Periodic Solutions to the Navier-Stokes Equations. (deposited 16 Feb 2024 07:59) [Gegenwärtig angezeigt]
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