Partial Differential Equations and Fluid Mechanics 1st Edition by James Robinson ISBN 978-1108460965 1108460968

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Product details: 

ISBN 10:  1108460968

ISBN 13: 978-1108460965

Author: James C. Robinson

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.

Table of contents: 

1 Shear flows and their attractors

M. Boukrouche & G. Lukaszewicz

2 Mathematical results concerning unsteady flows of chemically reacting incompressible fluids

M. Bulíček, J. Málek, & K.R. Rajagopal

3 The uniqueness of Lagrangian trajectories in

Navier-Stokes flows

M. Dashti & J.C. Robinson

4 Some controllability results in fluid mechanics

E. Fernandez-Cara

5 Singularity formation and separation phenomena in boundary layer theory

F. Gargano, M.C. Lombardo, M. Sammartino, & V. Sciacca

6 Partial regularity results for solutions of the Navier-Stokes system

I. Coward

7 Anisotropic Navier-Stokes equations in a bounded cylindrical domain

M. Paicu & G. Raugel

8 The regularity problem for the three-dimensional

Navier-Stokes equations

J.C. Robinson & W. Sadowski

9 Contour dynamics for the surface quasi-geostrophic equation

J.L. Rodrigo

10 Theory and applications of statistical solutions of the

Navier-Stokes equations

R. Rose

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Tags: James Robinson, Partial Differential, Fluid Mechanics