O Proceedings of the

Fifth Winter School


PASEKY (Czech Republic)
December 6 - 14, 1997

Published on 14 July, 1998


Advanced topics in theoretical fluid mechanics

Josef Malek (Ed)
Jindrich Necas (Ed)
Mirko Rokyta (Ed)

Pitman Research Notes In Mathematics Series 392
Addison Wesley Longman

1st Edition   1998     224 pages (est.)
ISBN 0-582-36803-0
Price GBP 31 (Paperback)

Title page

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This volume consists of four contributions based on a series of lectures delivered at the Fifth Winter School on Mathematical Theory in Fluid Mechanics, held in Paseky nad Jizerou, Czech Republic, from December 6-14, 1997. The contributions have been written by the main lecturers of the school, and concern various significant topics in the field of theoretical fluid mechanics.

Specifically, Bardos presents mathematical studies of various evolutionary models of fluids that capture the motions of gases and liquids on different scales starting from molecules and rarefied gases, continuing to fluids and gases at the continuum level and finishing with fluids in turbulent regimes. Besides the mathematical analysis of particular systems on their own, a great deal of attention is devoted to the passage from one scale to another. Dafermos provides a worthwhile introduction to the foundation of classical continuum physics built on a precise and general mathematical basis which enables one to present arguments in a very transparent way. Novotný investigates systematically the properties of the steady-state transport equations with the emphasis on flows in exterior domains. Finally, Solonnikov illustrates in a pedagogical way his approach to the non-simple analysis of free boundary problems in fluid mechanics by considering three model examples for the steady-state Navier-Stokes equations.

Readership: Applied mathematicians, researchers in theoretical fluid mechanics, analysts in partial differential equations.



Claude Bardos      (pp. 1-88)
From molecules to turbulence - an overview of multiscale analysis in fluid dynamics

Constantine M Dafermos     (pp. 89-117)
Balance laws in continuum physics

Antonín Novotný     (pp. 118-146)
On the steady transport equation

Vsevolod A Solonnikov     (pp. 147-212)
Stationary free boundary problems for the Navier-Stokes equations

About the authors

Josef Malek's affiliation: Charles University, Prague,

Jindrich Necas's affiliation: Charles University, Prague,

Mirko Rokyta's affiliation: Charles University, Prague,