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El. knyga: Partial Differential Equations in Fluid Mechanics

Edited by (Princeton University, New Jersey), Edited by (University of Warwick), Edited by (University of Warwick)
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The Euler and Navier–Stokes equations are the fundamental mathematical models of fluid mechanics, and their study remains central in the modern theory of partial differential equations. This volume of articles, derived from the workshop 'PDEs in Fluid Mechanics' held at the University of Warwick in 2016, serves to consolidate, survey and further advance research in this area. It contains reviews of recent progress and classical results, as well as cutting-edge research articles. Topics include Onsager's conjecture for energy conservation in the Euler equations, weak-strong uniqueness in fluid models and several chapters address the Navier–Stokes equations directly; in particular, a retelling of Leray's formative 1934 paper in modern mathematical language. The book also covers more general PDE methods with applications in fluid mechanics and beyond. This collection will serve as a helpful overview of current research for graduate students new to the area and for more established researchers.

This volume, derived from the 'PDEs in Fluid Mechanics' workshop held at the University of Warwick in 2016, serves to consolidate and advance work in mathematical fluid dynamics. Consisting of surveys and original research, it will be a valuable resource for both established researchers and graduate students seeking an overview of current developments.

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A selection of survey articles and original research papers in mathematical fluid mechanics, for both researchers and graduate students.
List of contributors
vii
Preface xi
1 Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier---Stokes equations
1(19)
C. Bardos
2 Time-periodic flow of a viscous liquid past a body
20(30)
G.P. Galdi
M. Kyed
3 The Rayleigh---Taylor instability in buoyancy-driven variable density turbulence
50(18)
J.D. Gibbon
P. Rao
C.P. Caulfield
4 On localization and quantitative uniqueness for elliptic partial differential equations
68(29)
G. Camliyurt
I. Kukavica
F. Wang
5 Quasi-invariance for the Navier---Stokes equations
97(16)
K. Ohkitani
6 Leray's fundamental work on the Navier---Stokes equations: a modern review of "Sur le mouvement d'un liquide visqueux emplissant l'espace"
113(91)
W.S. Ozanski
B.C. Pooley
7 Stable mild Navier---Stokes solutions by iteration of linear singular Volterra integral equations
204(20)
R. Rautmann
8 Energy conservation in the 3D Euler equations on T2 × R+
224(28)
J.C. Robinson
J.L. Rodrigo
J.W.D. Skipper
9 Regularity of Navier-Stokes flows with bounds for the velocity gradient along streamlines and an effective pressure
252(16)
C. V. Tran
X. Yu
10 A direct approach to Gevrey regularity on the half-space
268(21)
I. Kukavica
V. Vicol
11 Weak-Strong Uniqueness in Fluid Dynamics
289
E. Wiedemann
Charles L. Fefferman is the Herbert Jones Professor in the Mathematics Department at Princeton University, New Jersey. He was awarded the Fields Medal in 1978. James C. Robinson is a Professor of Mathematics at the University of Warwick. He is also a Royal Society University Research Fellow and an EPSRC Leadership Fellow. José L. Rodrigo is a Professor of Mathematics at the University of Warwick, and has been awarded an ERC Consolidator Grant.
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