Lp-Theory for Incompressible Newtonian Flows

Energy Preserving Boundary Conditions, Weakly Singular Domains
2013
ISBN: 978-3-658-01051-5
Verlag: Springer

Buch, Englisch, 183 Seiten, Format (B × H): 148 mm x 210 mm, Gewicht: 2604 g

This thesis is devoted to the study of the basic equations of fluid dynamics. First Matthias Köhne focuses on the derivation of a class of boundary conditions, which is based on energy estimates, and, thus, leads to physically relevant conditions. The derived class thereby contains many prominent artificial boundary conditions, which have proved to be suitable for direct numerical simulations involving artificial boundaries. The second part is devoted to the development of a complete Lp-theory for the resulting initial boundary value problems in bounded smooth domains, i.e. the Navier-Stokes equations complemented by one of the derived energy preserving boundary conditions. Finally, the third part of this thesis focuses on the corresponding theory for bounded, non-smooth domains, where the boundary of the domain is allowed to contain a finite number of edges, provided the smooth components of the boundary that meet at such an edge are locally orthogonal.

Zielgruppe

Research

Autoren/Hrsg.

Köhne, Matthias

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik

Inhaltsverzeichnis

Navier-Stokes Equations.- Energy Preserving Boundary Condition.- Weakly Singular Domain.- Maximal Lp-Regularity.

Über Autor(innen)

Matthias Köhne earned a doctorate of Mathematics under the supervision of Prof. Dr. Dieter Bothe at the Department of Mathematics at TU Darmstadt, where his research was supported by the cluster of excellence ''Center of Smart Interfaces'' and the international research training group ''Mathematical Fluid Dynamics''.