Mathematical Aspects of Fluid Mechanics

A selection of surveys and original research papers in mathematical fluid mechanics arising from a 2010 workshop held in Warwick.

James C. Robinson (Edited by), José L. Rodrigo (Edited by), Witold Sadowski (Edited by)

9781107609259, Cambridge University Press

Paperback / softback, published 18 October 2012

276 pages, 17 b/w illus. 3 tables
22.6 x 15.2 x 1.8 cm, 0.41 kg

The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier–Stokes equations feature prominently: the reader will find new results concerning feedback stabilisation, stretching and folding, and decay in norm of solutions to these fundamental equations of fluid motion. Other topics covered include new models for turbulent energy cascade, existence and uniqueness results for complex fluids and certain interesting solutions of the SQG equation. The result is an accessible collection of survey articles and more traditional research papers that will serve both as a helpful overview for graduate students new to the area and as a useful resource for more established researchers.

Preface
List of contributors
1. Towards fluid equations by approximate deconvolution models L. C. Berselli
2. On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph M. Bulí?ek, P. Gwiazda, J. Málek, K. R. Rajagopal and A. ?wierczewska-Gwiazda
3. A continuous model for turbulent energy cascade A. Cheskidov, R. Shvydkoy and S. Friedlander
4. Remarks on complex fluid models P. Constantin
5. A naive parametrization for the vortex-sheet problem A. Castro, D. Córdoba and F. Gancedo
6. Sharp and almost-sharp fronts for the SQG equation C. L. Fefferman
7. Feedback stabilization for the Navier–Stokes equations: theory and calculations A. V. Fursikov and A. A. Kornev
8. Interacting vortex pairs in inviscid and viscous planar flows T. Gallay
9. Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier–Stokes equations J. D. Gibbon and D. D. Holm
10. Exploring symmetry plane conditions in numerical Euler solutions R. M. Kerr and M. D. Bustamante
11. On the decay of solutions of the Navier–Stokes system with potential forces I. Kukavica
12. Leray–Hopf solutions to Navier–Stokes equations with weakly converging initial data G. Seregin.

Subject Areas: Mechanics of fluids [TGMF], Engineering thermodynamics [TGMB], Fluid mechanics [PHDF], Integral calculus & equations [PBKL], Differential calculus & equations [PBKJ]