Partial Differential Equations and Fluid Mechanics

doi:10.1017/CBO9781139107112

Recent years have seen considerable research activity at the interface of mathematics and fluid mechanics, particularly partial differential equations. The 2007 workshop at the University of Warwick was organised to consolidate, survey and further advance the subject. This volume is an outgrowth of that workshop. It consists of a number of reviews and a selection of more traditional research articles. The result is an accessible summary of a wide range of active research topics written by leaders in their field, together with some exciting new results. The book serves as both a helpful overview for graduate students new to the area and a useful resource for more established researchers.

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Contents

Frontmatter
pp i-vi
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Contents
pp vii-viii
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Preface
pp ix-ix
- By James C. Robinson, Warwick, José L. Rodrigo, Warwick
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List of contributors
pp x-xii
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1 - Shear flows and their attractors
pp 1-25
- By M. Boukrouche, University of Saint-Etienne, G. Łukaszewicz, University of Warsaw
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2 - Mathematical results concerning unsteady flows of chemically reacting incompressible fluids
pp 26-53
- By M. Bulíček, University, Faculty, J. Málek, University, Faculty, K.R. Rajagopal, University, College Station
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3 - The uniqueness of Lagrangian trajectories in Navier–Stokes flows
pp 54-63
- By M. Dashti, University of Warwick, J.C. Robinson, University of Warwick
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4 - Some controllability results in fluid mechanics
pp 64-80
- By E. Fernández-Cara, Universidad de Sevilla
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5 - Singularity formation and separation phenomena in boundary layer theory
pp 81-120
- By F. Gargano, Department of Mathematics, Via Archirafi 34, 90123 Palermo. Italy, M.C. Lombardo, Department of Mathematics, Via Archirafi 34, 90123 Palermo. Italy, M. Sammartino, Department of Mathematics, Via Archirafi 34, 90123 Palermo. Italy, V. Sciacca, Department of Mathematics, Via Archirafi 34, 90123 Palermo. Italy
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6 - Partial regularity results for solutions of the Navier–Stokes system
pp 121-145
- By I. Kukavica, University of Southern California
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7 - Anisotropic Navier–Stokes equations in a bounded cylindrical domain
pp 146-184
- By M. Paicu, Univ Paris-Sud and CNRS, G. Raugel, CNRS and Univ Paris-Sud
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8 - The regularity problem for the three-dimensional Navier–Stokes equations
pp 185-206
- By J.C. Robinson, University of Warwick, W. Sadowski, University of Warsaw
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9 - Contour dynamics for the surface quasi-geostrophic equation
pp 207-227
- By J.L. Rodrigo, University of Warwick
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10 - Theory and applications of statistical solutions of the Navier–Stokes equations
pp 228-257
- By R. Rosa, Universidade Federal do Rio de Janeiro
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Partial Differential Equations and Fluid Mechanics

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Contents

Frontmatter
pp i-vi

Contents
pp vii-viii

Preface
pp ix-ix

List of contributors
pp x-xii

1 - Shear flows and their attractors
pp 1-25

2 - Mathematical results concerning unsteady flows of chemically reacting incompressible fluids
pp 26-53

3 - The uniqueness of Lagrangian trajectories in Navier–Stokes flows
pp 54-63

4 - Some controllability results in fluid mechanics
pp 64-80

5 - Singularity formation and separation phenomena in boundary layer theory
pp 81-120

6 - Partial regularity results for solutions of the Navier–Stokes system
pp 121-145

7 - Anisotropic Navier–Stokes equations in a bounded cylindrical domain
pp 146-184

8 - The regularity problem for the three-dimensional Navier–Stokes equations
pp 185-206

9 - Contour dynamics for the surface quasi-geostrophic equation
pp 207-227

10 - Theory and applications of statistical solutions of the Navier–Stokes equations
pp 228-257

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Partial Differential Equations and Fluid Mechanics

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