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The Stokes and Navier-Stokes equations in layer domains with and without a free surface

Below, Lorenz von (2014)
The Stokes and Navier-Stokes equations in layer domains with and without a free surface.
Technische Universität Darmstadt
Ph.D. Thesis, Primary publication

Abstract

This thesis is concerned with certain aspects of the Stokes- and Navier-Stokes equations in layer domains with and without a free surface. We investigate the Stokes equations in layer domains in the endpoints L1 and Linfty of the scale of Lebesgue spaces Lp and show that the Stokes operator in solenoidal subspaces of L1 and Linfty generates a holomorphic semigroup if and only if the spacial dimension of the layer dimension is two. In the last chapter we investigate the singular limit of vanishing surface tension for a free boundary problem for the Navier-Stokes equations and show convergence of solutions in the Lp maximal regularity space.

Item Type: Ph.D. Thesis
Erschienen: 2014
Creators: Below, Lorenz von
Type of entry: Primary publication
Title: The Stokes and Navier-Stokes equations in layer domains with and without a free surface
Language: English
Referees: Geißert, PD Dr. Matthias ; Hieber, Prof. Dr. Matthias ; Shibata, Prof. Dr. Yoshihiro
Date: 2014
Refereed: 16 October 2014
URL / URN: http://tuprints.ulb.tu-darmstadt.de/4228
Abstract:

This thesis is concerned with certain aspects of the Stokes- and Navier-Stokes equations in layer domains with and without a free surface. We investigate the Stokes equations in layer domains in the endpoints L1 and Linfty of the scale of Lebesgue spaces Lp and show that the Stokes operator in solenoidal subspaces of L1 and Linfty generates a holomorphic semigroup if and only if the spacial dimension of the layer dimension is two. In the last chapter we investigate the singular limit of vanishing surface tension for a free boundary problem for the Navier-Stokes equations and show convergence of solutions in the Lp maximal regularity space.
Alternative Abstract:
Alternative abstract Language

In dieser Dissertation beschäftigen wir uns mit Aspekten der Stokes- und Navier-Stokes-Gleichungen in Schichtgebieten mit oder ohne freiem Rand. Wir untersuchen die Stokes-Gleichungen in Schichtgebieten in den Endpunkten L1 und Linfty der Skala von Lebesgue-Räumen Lp und zeigen, dass der Stokes-Operator in Schichtgebieten in divergenzfreien Unterräumen von L1 bzw. Linfty genau dann eine holomorphe Halbgruppe erzeugt, wenn die Raumdimension des Schichtgebietes zwei ist. Im letzten Kapitel untersuchen wir den singulären Grenzwert verschwindender Oberflächenspannung für ein freies Randwertproblem der Navier-Stokes-Gleichungen und zeigen Konvergenz der Lösungen im korrespondierenden Raum maximaler Lp Regularität.

German
URN: urn:nbn:de:tuda-tuprints-42288
Classification DDC: 500 Science and mathematics > 510 Mathematics
Divisions: 04 Department of Mathematics > Analysis
04 Department of Mathematics
Date Deposited: 09 Nov 2014 20:55
Last Modified: 15 Feb 2016 15:26
PPN:
Referees: Geißert, PD Dr. Matthias ; Hieber, Prof. Dr. Matthias ; Shibata, Prof. Dr. Yoshihiro
Refereed / Verteidigung / mdl. Prüfung: 16 October 2014
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