Contributions to Current Challenges in Mathematical Fluid Mechanics (Paperback, Softcover reprint of the original 1st ed. 2004)

This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the Navier-Stokes equations, for compressible and incompressible fluids, and to related questions. All results given here are new and represent a noticeable contribution to the subject. One of the most famous predictions of the Kolmogorov theory of turbulence is the so-called Kolmogorov-obukhov five-thirds law. As is known, this law is heuristic and, to date, there is no rigorous justification. The article of A. Biryuk deals with the Cauchy problem for a multi-dimensional Burgers equation with periodic boundary conditions. Estimates in suitable norms for the corresponding solutions are derived for "large" Reynolds numbers, and their relation with the Kolmogorov-Obukhov law are discussed. Similar estimates are also obtained for the Navier-Stokes equation. In the late sixties J. L. Lions introduced a "perturbation" of the Navier Stokes equations in which he added in the linear momentum equation the hyper dissipative term (-Ll),Bu, f3 ~ 5/4, where Ll is the Laplace operator. This term is referred to as an "artificial" viscosity. Even though it is not physically moti vated, artificial viscosity has proved a useful device in numerical simulations of the Navier-Stokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global well-posedness of a modification of the Navier Stokes equation similar to that introduced by Lions, but where now the original dissipative term -Llu is replaced by (-Ll)O:u, 0 S Ct < 5/4.

General

Imprint:	Birkhauser Verlag AG
Country of origin:	Switzerland
Series:	Advances in Mathematical Fluid Mechanics
Release date:	October 2012
First published:	October 2012
Editors:	Giovanni P. Galdi • John G. Heywood • Rolf Rannacher
Dimensions:	235 x 155 x 8mm (L x W x T)
Format:	Paperback
Pages:	152
Edition:	Softcover reprint of the original 1st ed. 2004
ISBN-13:	978-3-03-489606-1
Categories:	Books > Science & Mathematics > Mathematics > Calculus & mathematical analysis > Differential equations Books > Science & Mathematics > Mathematics > Applied mathematics > General Books > Science & Mathematics > Physics > Classical mechanics > General
LSN:	3-03-489606-9
Barcode:	9783034896061

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