Dokument: Resolvent Estimates for 2D Contact Line Dynamics and Stability Analysis for Active Fluids
| Titel: | Resolvent Estimates for 2D Contact Line Dynamics and Stability Analysis for Active Fluids | |||||||
| URL für Lesezeichen: | https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=64304 | |||||||
| URN (NBN): | urn:nbn:de:hbz:061-20240201-142718-9 | |||||||
| Kollektion: | Dissertationen | |||||||
| Sprache: | Englisch | |||||||
| Dokumententyp: | Wissenschaftliche Abschlussarbeiten » Dissertation | |||||||
| Medientyp: | Text | |||||||
| Autor: | Bui, Christiane Anh-Nguyet [Autor] | |||||||
| Dateien: |
| |||||||
| Beitragende: | Prof.Dr. Saal, Jürgen [Gutachter] Priv.-Doz. Dr. Köhne, Matthias [Gutachter] | |||||||
| Stichwörter: | Partial Differential Equations; Functional Analysis; Contact Line Dynamics; Active Fluids; Fluid Dynamics | |||||||
| Dokumententyp (erweitert): | Dissertation | |||||||
| Dewey Dezimal-Klassifikation: | 500 Naturwissenschaften und Mathematik » 510 Mathematik | |||||||
| Beschreibung: | In this thesis we consider two different models known from fluid dynamics which are based on Navier-Stokes equations.
The first model is devoted to the 2D contact line dynamics investigating the contact point between fluid and solid phases. Since the fluid and solid phases are moving within time, it is necessary to transform this model to a fixed domain in order to apply known strategies. This leads to a system of Stokes equations subject to transformed free and partial slip boundary conditions which are considered on the sector. Then linear analysis is performed for the resolvent Stokes system leading to the existence of weak solutions. The main result states that the solution triple fulfills corresponding resolvent estimates. The second model is an active fluid continuum model which describes the motion of self-propelled organisms of high concentration in fluids. This model is based on generalized Navier-Stokes equations having a leading fourth order term which is responsible for global wellposedness. Here, we consider the active fluid continuum model on a bounded domain subject to periodic boundary conditions in Lebesgue spaces with p = 2 in two and three dimensions. Two stationary states are considered: the disordered isotropic state and the ordered polar state. In this thesis, we focus on the stability analysis of the ordered polar state which indeed forms a manifold. Furthermore, the existence of a global attractor for the active fluid continuum model is established. Several properties of the global attractor are proved, to be precise we show injectivity and finite dimension of the global attractor. At last we even prove the existence of an inertial manifold in two dimensions which has even the stronger property of attracting solutions exponentially. | |||||||
| Lizenz: |  Dieses Werk ist lizenziert unter einer Creative Commons Namensnennung 4.0 International Lizenz | |||||||
| Fachbereich / Einrichtung: | Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik | |||||||
| Dokument erstellt am: | 01.02.2024 | |||||||
| Dateien geändert am: | 01.02.2024 | |||||||
| Promotionsantrag am: | 31.07.2023 | |||||||
| Datum der Promotion: | 26.09.2023 |
