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El. knyga: Mathematical Aspects of Fluid Mechanics

Edited by (University of Warwick), Edited by (Uniwersytet Warszawski, Poland), Edited by (University of Warwick)

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"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."--Publisher's website.

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A selection of surveys and original research papers in mathematical fluid mechanics arising from a 2010 workshop held in Warwick.
Preface ix
List of Contributors
xi
1 Towards fluid equations by approximate deconvolution models
1(22)
L.C. Berselli
2 On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph
23(29)
M. Bulicek
P. Gwiazda
J. Malek
K.R. Rajagopal
A. Swierczewska-Gwiazda
3 A continuous model for turbulent energy cascade
52(18)
A. Cheskidov
R. Shvydkoy
S. Friedlander
4 Remarks on complex fluid models
70(18)
P. Constantin
5 A naive parametrization for the vortex-sheet problem
88(28)
A. Castro
D. Cordoba
F. Gancedo
6 Sharp and almost-sharp fronts for the SQG equation
116(14)
C.L. Fefferman
7 Feedback stabilization for the Navier-Stokes equations: theory and calculations
130(43)
A.V. Fursikov
A.A. Kornev
8 Interacting vortex pairs in inviscid and viscous planar flows
173(28)
T. Gallay
9 Stretching and folding diagnostics in solutions of the three-dimensional Euler and Navier-Stokes equations
201(20)
J.D. Gibbon
D.D. Holm
10 Exploring symmetry plane conditions in numerical Euler solutions
221(14)
R.M. Kerr
M.D. Bustamante
11 On the decay of solutions of the Navier-Stokes system with potential forces
235(16)
I. Kukavica
12 Leray-Hopf solutions to Navier-Stokes equations with weakly converging initial data
251
G. Seregin
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. José L. Rodrigo is an Associate Professor in Mathematics at the University of Warwick. Witold Sadowksi is an Assistant Professor at the University of Warsaw.