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Including previously unpublished, original research material, this
comprehensive book analyses topics of fundamental importance in
theoretical fluid mechanics. The five papers appearing in this
volume are centred around the mathematical theory of the
Navier-Stokes equations (incompressible and compressible) and
certain selected non-Newtonian modifications.
The five papers collected in this volume are the content of a
series of lectures delivered at the Second Winter School in Fluid
Dynamics held in Paseky, Czech Republic, from November 29 to
December 4 1992, concerning different fields in theoretical fluid
mechanics. The lectures present recent results of the authors'
investigations and the majority of the contributions are original
results which are not published elsewhere. Specifically, Galdi
studies the two-dimensional exterior problem for the steady-state
Navier-Stokes equations and Matsumura deals with some basic
questions related to existence and stability of one-dimensional
flow of compressible fluids. Both papers represent a difficult
mathematical approach to solving deep problems. The paper by
Girault furnishes a detailed and comprehensive analysis of the
Stokes problem in exterior domains that has important consequences
on numerical analysis. Litvinov's paper is dedicated to existence
theory for a class of equations describing the motions of certain
non classical fluids. Finally, the contribution from Rajagopal is a
detailed and updated review of non-Newtonian fluid mechanics with
emphasis on the different types of constitutive equations.
This volume consists of four contributions that are based on a
series of lectures delivered by Jens Frehse. Konstantin Pikeckas,
K.R. Rajagopal and Wolf von Wahl t the Fourth Winter School in
Mathematical Theory in Fluid Mechanics, held in Paseky, Czech
Republic, from December 3-9, 1995. In these papers the authors
present the latest research and updated surveys of relevant topics
in the various areas of theoretical fluid mechanics.
Specifically, Frehse and Ruzicka study the question of the
existence of a regular solution to Navier-Stokes equations in five
dimensions by means of weighted estimates. Pileckas surveys recent
results regarding the solvability of the Stokes and Navier-Stokes
system in domains with outlets at infinity. K.R. Rajagopal presents
an introduction to a continuum approach to mixture theory with the
emphasis on the constitutive equation, boundary conditions and
moving singular surface. Finally, Kaiser and von Wahl bring new
results on stability of basic flow for the Taylor-Couette problem
in the small-gap limit. This volume would be indicated for those in
the fields of applied mathematicians, researchers in fluid
mechanics and theoretical mechanics, and mechanical engineers.
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