Mathematical Aspects of Fluid Mechanics

Mathematical Aspects of Fluid Mechanics

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Description

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.show more

Product details

  • Electronic book text
  • CAMBRIDGE UNIVERSITY PRESS
  • Cambridge University Press (Virtual Publishing)
  • Cambridge, United Kingdom
  • 17 b/w illus. 3 tables
  • 1139575457
  • 9781139575454

About James C. Robinson

James C. Robinson is a Professor of Mathematics at the University of Warwick. He is an EPSRC Leadership Fellow and has previously held a Royal Society University Research Fellowship. Jose L. Rodrigo is an Associate Professor in Mathematics at the University of Warwick. Witold Sadowksi is an Assistant Professor at the University of Warsaw.show more

Table of contents

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. Bulicek, P. Gwiazda, J. Malek, K. R. Rajagopal and A. Swierczewska-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. Cordoba 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.show more