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On the primitive equations and the hydrostatic Stokes operator

Gries, Mathis Yannik (2018):
On the primitive equations and the hydrostatic Stokes operator.
Darmstadt, Technische Universität, [Online-Edition: https://tuprints.ulb.tu-darmstadt.de/7675],
[Ph.D. Thesis]

Abstract

The primitive equations for the atmosphere and ocean, as well as its linearization, called the hydrostatic Stokes equation, are considered. The study of the latter problem in spaces of Lp- and anisotropic Lp-type yields results such as parabolic decay estimates as well as the property of maximal regularity. Applying these results to the full nonlinear problem yields the existence of unique global strong solutions to the primitive equations for a large class of initial data.

Item Type: Ph.D. Thesis
Erschienen: 2018
Creators: Gries, Mathis Yannik
Title: On the primitive equations and the hydrostatic Stokes operator
Language: English
Abstract:

The primitive equations for the atmosphere and ocean, as well as its linearization, called the hydrostatic Stokes equation, are considered. The study of the latter problem in spaces of Lp- and anisotropic Lp-type yields results such as parabolic decay estimates as well as the property of maximal regularity. Applying these results to the full nonlinear problem yields the existence of unique global strong solutions to the primitive equations for a large class of initial data.

Place of Publication: Darmstadt
Divisions: 04 Department of Mathematics
04 Department of Mathematics > Analysis
04 Department of Mathematics > Analysis > Angewandte Analysis
04 Department of Mathematics > Analysis > Partial Differential Equations and Applications
Date Deposited: 26 Aug 2018 19:55
Official URL: https://tuprints.ulb.tu-darmstadt.de/7675
URN: urn:nbn:de:tuda-tuprints-76754
Referees: Hieber, Prof. Dr. Matthias and Giga, Prof. Dr. Yoshikazu
Refereed / Verteidigung / mdl. Prüfung: 5 July 2018
Alternative Abstract:
Alternative abstract Language
In dieser Arbeit werden die sogenannten "primitive equations" und ihre Linearisierung, genannt die hydrostatische Stokes-Gleichung, behandelt. Das Studium des letzteren Problems in Räumen vom Lp- und anisotropischem Lp-Typ liefert parabolische Abkling-Abschätzungen sowie die Eigenschaft der maximalen Regularität. Die Anwendung dieser Ergebnisse auf das vollständige nichtlineare Problem liefert die Existenz von eindeutigen globalen starken Lösungen der primitive equations für eine große Klasse von Anfangsdaten.German
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