Dokument: The Stokes and Navier-Stokes Equations in Triebel-Lizorkin-Lorentz Spaces and on Uniform C^{2,1}-Domains

Titel:	The Stokes and Navier-Stokes Equations in Triebel-Lizorkin-Lorentz Spaces and on Uniform C^{2,1}-Domains
URL für Lesezeichen:	https://docserv.uni-duesseldorf.de/servlets/DocumentServlet?id=52595
URN (NBN):	urn:nbn:de:hbz:061-20200310-105927-8
Kollektion:	Dissertationen
Sprache:	Deutsch
Dokumententyp:	Wissenschaftliche Abschlussarbeiten » Dissertation
Medientyp:	Text
Autor:	Hobus, Pascal [Autor]
Dateien:	[Dateien anzeigen] Adobe PDF [Details] 3,31 MB in einer Datei [ZIP-Datei erzeugen] Dateien vom 09.03.2020 / geändert 09.03.2020
Beitragende:	Prof. Dr. Saal, Jürgen [Gutachter] Prof. Dr. Farwig, Reinhard [Gutachter]
Stichwörter:	Navier-Stokes equations, Triebel-Lizorkin-Lorentz spaces
Dewey Dezimal-Klassifikation:	500 Naturwissenschaften und Mathematik » 510 Mathematik
Beschreibung:	The subject of this thesis is the mathematical Navier-Stokes equations in a domain on some fixed time interval and the Stokes equations that we receive by leaving out the nonlinear term. We treat these equations subject to partial slip type boundary conditions. This class of boundary conditions contains Navier boundary conditions and the perfect slip boundary condition, which equals the vorticity condition in space dimension three. We prove well-posedness of the Stokes equations via analytic semigroup theory in the setting of Lebesgue spaces for a large class of domains with uniform C^{2,1}-boundary. This class particularly includes domains, where the classical Helmholtz decomposition fails to exist, e.g., sector-like domains with a smoothed vertex and an opening angle which is large enough. Further results on the Stokes resolvent problem and applications to the Navier-Stokes equations on domains are included in the presented outcomes. Moreover, for the case that the domain is the whole space, we prove existence and uniqueness of maximal strong solutions to the Navier-Stokes equations in the scale of Triebel-Lizorkin-Lorentz spaces. This scale contains many important function spaces such as Sobolev-Slobodeckii spaces, Bessel-potential spaces, Lorentz spaces and, in particular, Lebesgue spaces. Now the stated results concerning Triebel-Lizorkin-Lorentz spaces yield corresponding results simultaneously for all the spaces that one can find in this scale.
Lizenz:	Urheberrechtsschutz
Fachbereich / Einrichtung:	Mathematisch- Naturwissenschaftliche Fakultät » WE Mathematik » Angewandte Analysis
Dokument erstellt am:	10.03.2020
Dateien geändert am:	10.03.2020
Promotionsantrag am:	19.12.2019
Datum der Promotion:	05.03.2020