Recent Progress in the Theory of the Euler and Navier–Stokes Equations

doi:10.1017/CBO9781316407103

The rigorous mathematical theory of the Navier–Stokes and Euler equations has been a focus of intense activity in recent years. This volume, the product of a workshop in Venice in 2013, consolidates, surveys and further advances the study of these canonical equations. It consists of a number of reviews and a selection of more traditional research articles on topics that include classical solutions to the 2D Euler equation, modal dependency for the 3D Navier–Stokes equation, zero viscosity Boussinesq equations, global regularity and finite-time singularities, well-posedness for the diffusive Burgers equations, and probabilistic aspects of the Navier–Stokes equation. 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 both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

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Contents

Frontmatter
pp i-iv
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Dedication
pp v-vi
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Contents
pp vii-viii
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Preface
pp ix-x
- By James C. Robinson, University of Warwick, José L. Rodrigo, University of Warwick, Witold Sadowski, Uniwersytet Warszawski, Poland, Alejando Vidal López, Xi'an Jiaotong-Liverpool University, P. R. China
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List of contributors
pp xi-xiv
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1 - Classical solutions to the two-dimensional Euler equations and elliptic boundary value problems, an overview
pp 1-21
- By H. Beirão Da Veiga, Università di Pisa
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2 - Analyticity radii and the Navier–Stokes equations: recent results and applications
pp 22-36
- By Z. Bradshaw, University of British Columbia, Z. Grujić, University of Virginia, I. Kukavica, University of Southern California
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3 - On the motion of a pendulum with a cavity entirely filled with a viscous liquid
pp 37-56
- By G.P. Galdi, University of Pittsburgh, G. Mazzone, University of Pittsburgh
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4 - Modal dependency and nonlinear depletion in the three–dimensional Navier–Stokes equations
pp 57-76
- By J.D. Gibbon, Imperial College London
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5 - Boussinesq equations with zero viscosity or zero diffusivity: a review
pp 77-95
- By W. Hu, University of Southern California, I. Kukavica, University of Southern California, F. Wang, University of Southern California, M. Ziane, University of Southern California
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6 - Global regularity versus finite-time singularities: some paradigms on the effect of boundary conditions and certain perturbations
pp 96-125
- By A. Larios, University of Nebraska-Lincoln, E.S. Titi, Texas A&M University
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7 - Parabolic Morrey spaces and mild solutions of the Navier–Stokes equations. An interesting answer through a silly method to a stupid question
pp 126-136
- By P.G. Lemarié-rieusset, Université d’Évry
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8 - Well-posedness for the diffusive 3D Burgers equations with initial data in H½
pp 137-153
- By B.C. Pooley, University of Warwick, J.C. Robinson, University of Warwick
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9 - On the Fursikov approach to the moment problem for the three-dimensional Navier–Stokes equations
pp 154-174
- By J.C. Robinson, University of Warwick, A. Vidal-López, Xi'an Jiaotong-Liverpool University
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10 - Some probabilistic topics in the Navier–Stokes equations
pp 175-232
- By M. Romito, Università di Pisa
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Recent Progress in the Theory of the Euler and Navier–Stokes Equations

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Contents

Frontmatter
pp i-iv

Dedication
pp v-vi

Contents
pp vii-viii

Preface
pp ix-x

List of contributors
pp xi-xiv

1 - Classical solutions to the two-dimensional Euler equations and elliptic boundary value problems, an overview
pp 1-21

2 - Analyticity radii and the Navier–Stokes equations: recent results and applications
pp 22-36

3 - On the motion of a pendulum with a cavity entirely filled with a viscous liquid
pp 37-56

4 - Modal dependency and nonlinear depletion in the three–dimensional Navier–Stokes equations
pp 57-76

5 - Boussinesq equations with zero viscosity or zero diffusivity: a review
pp 77-95

6 - Global regularity versus finite-time singularities: some paradigms on the effect of boundary conditions and certain perturbations
pp 96-125

7 - Parabolic Morrey spaces and mild solutions of the Navier–Stokes equations. An interesting answer through a silly method to a stupid question
pp 126-136

8 - Well-posedness for the diffusive 3D Burgers equations with initial data in H½
pp 137-153

9 - On the Fursikov approach to the moment problem for the three-dimensional Navier–Stokes equations
pp 154-174

10 - Some probabilistic topics in the Navier–Stokes equations
pp 175-232

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Recent Progress in the Theory of the Euler and Navier–Stokes Equations

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