Dynamics of viscous compressible fluids

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Title:

Personal Author:

Feireisl, Eduard

Series:

Oxford lecture series in mathematics and its applications ; 26

Publication Information:

Oxford : Oxford University Press, 2004

ISBN:

9780198528388

Subject Term:

Viscous flow

Navier-Stokes equations

Fluid dynamics

Available:*

Library	Item Barcode	Call Number	Material Type	Item Category 1	Status
Searching... PSZ JB	30000010060045	QA929 F44 2004	Open Access Book	Book	Searching... Unknown
Searching... SPACE KL Main Library	30000010077196	QA929 F44 2004	Unknown	1:CHECKING	Searching... Unknown
Searching... SPACE Pulau Pinang Library	30000010077195	QA929 F44 2004	Unknown	1:CHECKING	Searching... Unknown

The book develops the most recent ideas and concepts of the mathematical theory of viscous, compressible and heat conducting fluids. Two main goals are pursued: (i) global existence theory within the framework of variational (weak) solutions for the full system of the Navier-Stokes equations supplemented with large data; and (ii) optimal existence results for the barotropic flows with respect to the available a priori estimates.The book is intended to be a compact and self-contained presentation of the most recent results of the mathematical theory of viscous compressible fluids. In order to place the text in better perspective, each chapter is concluded with a section devoted to historical notes including references to all important and new results. The material is by no means intended to be the last word on the subject but rather to indicate possible directions of future research. It is aimed at research mathematicians, theoretical physicists, engineers and graduate students.

Author Notes

Eduard Feireisl is a researcher at the Mathematical Institute of the Czech Academy of Sciences, Prague.

Preface	p. vii
Acknowledgement	p. xi
1 Physical background	p. 1
1.1 Kinematics, description of motion	p. 1
1.2 Balance laws	p. 3
1.3 Constitutive equations	p. 6
1.4 Barotropic flows	p. 13
1.5 The Navier-Stokes system	p. 15
1.6 Bibliographical notes	p. 17
2 Mathematical preliminaries	p. 20
2.1 Function spaces	p. 20
2.2 Weak convergence	p. 28
2.3 Vector functions of one real variable	p. 37
2.4 Bibliographical notes	p. 39
3 A priori estimates	p. 40
3.1 Estimates based on the maximum principle	p. 42
3.2 Total mass conservation	p. 44
3.3 Energy estimates	p. 44
3.4 Viscous dissipation	p. 46
3.5 A priori estimates--summary	p. 51
3.6 Bibliographical notes	p. 52
4 Variational solutions	p. 54
4.1 The equation of continuity	p. 54
4.2 Momentum equation	p. 66
4.3 Thermal energy equation	p. 74
4.4 Bibliographical notes	p. 83
5 Pressure and temperature estimates	p. 86
5.1 Local pressure estimates	p. 86
5.2 Temperature estimates	p. 94
5.3 Bibliographical notes	p. 99
6 Fundamental ideas	p. 101
6.1 The effective viscous pressure	p. 103
6.2 A result of P.-L. Lions on weak continuity	p. 103
6.3 Weak continuity via compensated compactness	p. 105
6.4 The oscillations defect measure	p. 111
6.5 Renormalized solutions revisited	p. 116
6.6 Propagation of oscillations	p. 118
6.7 Weak stability revisited	p. 127
6.8 Limits of bounded sequences in L[superscript 1]	p. 137
6.9 Bibliographical notes	p. 140
7 Global existence	p. 142
7.1 Statement of the main result	p. 143
7.2 The approximation scheme	p. 147
7.3 The Faedo-Galerkin approximations	p. 149
7.4 Vanishing artificial viscosity	p. 175
7.5 Vanishing artificial pressure	p. 187
7.6 Bibliographical notes	p. 198
Bibliography	p. 201
Index	p. 209

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Author Notes

Table of Contents