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Navier-Stokes Flow in Partially Periodic Domains

Sierke Verlag,
48,00 € Preisreferenz Lieferbar in 2-3 Tagen


One of the fundamental models in fluid dynamics are the Navier-Stokes
equations, modelling the fluid flow of an incompressible Newtonian
fluid. Despite recent progress in scientific research, the Navier-Stokes
equations continue to be far from well-understood. Nevertheless, during
the last two decades many results have appeared in the literature
dealing with special problems that arise in the case of unbounded
domains, where compactness arguments break down. Typically, these
results impose in one way or the other a decay condition towards
spatial infinity. However, there are not many results concerning
(partially) spatially periodic setups, e.g., periodic flows in pipes with
periodically repetitive profile or models for certain fluids with intrinsical
periodic structures.
In his thesis, Jonas Sauer uses a wide spectrum of mathematical tools
in order to develop a full theory in weighted Lebesgue spaces for such
partially periodic set-ups. The concept of Muckenhoupt weights on
locally compact abelian groups is introduced and its connection to
partially periodic evolution equations is highlighted. The author then
continues to establish weighted resolvent estimates for solutions to the
linear Stokes equations in different domains such as the whole space,
the half space and cylindrical domains. Also weak Neumann problems
are treated in order to introduce the Helmholtz-Leray projection.
In the last part, the author investigates a non-linear, partially periodic
model describing the dynamics of nematic liquid crystal flows. Here,
the full power of the linear theory is exploited by proving maximal
regularity of the partially periodic Stokes operator via the connection
of Muckenhoupt weights to evolution equations.


Titel: Navier-Stokes Flow in Partially Periodic Domains
Autoren/Herausgeber: Jonas Sauer
Ausgabe: 1. Auflage

ISBN/EAN: 9783868447552

Seitenzahl: 228
Format: 25 x 17,6 cm
Produktform: Taschenbuch/Softcover
Gewicht: 430 g
Sprache: Englisch

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