| Contributions to Current Challenges in Mathematical Fluid Mechanics 2004 Edition Contributor(s): Galdi, Giovanni P. (Editor), Heywood, John G. (Editor), Rannacher, Rolf (Editor) |
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ISBN: 3764371048 ISBN-13: 9783764371043 Publisher: Birkhauser OUR PRICE: $52.24 Product Type: Hardcover - Other Formats Published: July 2004 Annotation: The mathematical theory of the Navier-Stokes equations presents still fundamental open questions that represent as many challenges for the interested mathematicians. This volume collects a series of articles whose objective is to furnish new contributions and ideas to these questions, with particular regard to turbulence modelling, regularity of solutions to the initial-value problem, flow in region with an unbounded boundary and compressible flow. Contributors: A. Biryuk D. Chae and J. Lee A. Dunca, V. John and W.J. Layton T. Hishida T. Leonaviciene and K. Pileckas |
| Additional Information |
| BISAC Categories: - Gardening - Science | Mechanics - General - Mathematics | Differential Equations - General |
| Dewey: 515.353 |
| LCCN: 2004055052 |
| Series: Advances in Mathematical Fluid Mechanics |
| Physical Information: 0.44" H x 6.14" W x 9.21" (0.90 lbs) 152 pages |
| Descriptions, Reviews, Etc. |
| Publisher Description: 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 |