On the primitive equations and the hydrostatic Stokes operator

Gries, Mathis Yannik (2018)
On the primitive equations and the hydrostatic Stokes operator.
Technische Universität Darmstadt
Ph.D. Thesis, Primary publication

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Item Type:

Ph.D. Thesis

Type of entry:

Primary publication

Title:

On the primitive equations and the hydrostatic Stokes operator

Language:

English

Referees:

Hieber, Prof. Dr. Matthias ; Giga, Prof. Dr. Yoshikazu

Date:

2018

Place of Publication:

Darmstadt

Date of oral examination:

5 July 2018

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.

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

URN:

urn:nbn:de:tuda-tuprints-76754

Classification DDC:

500 Science and mathematics > 510 Mathematics

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:

23 Aug 2018 10:16

Last Modified:

26 Feb 2020 15:49

URI: