Including previously unpublished, original research material, this comprehensive book analyses topics of fundamental importance in theoretical fluid mechanics.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.