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＜電子ブック＞
Contributions to Current Challenges in Mathematical Fluid Mechanics / edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher
(Advances in Mathematical Fluid Mechanics. ISSN:22970339)

版	1st ed. 2004.
出版者	(Basel : Birkhäuser Basel : Imprint: Birkhäuser)
出版年	2004
本文言語	英語
大きさ	VIII, 152 p : online resource
著者標目	Galdi, Giovanni P editor Heywood, John G editor Rannacher, Rolf editor SpringerLink (Online service)
件　名	LCSH:Physics LCSH:Differential equations LCSH:Mathematical physics FREE:Classical and Continuum Physics FREE:Differential Equations FREE:Mathematical Methods in Physics
一般注記	On Multidimensional Burgers Type Equations with Small Viscosity -- 1. Introduction -- 2. Upper estimates -- 3. Lower estimates -- 4. Fourier coefficients -- 5. Low bounds for spatial derivatives of solutions of the Navier—Stokes system -- References -- On the Global Well-posedness and Stability of the Navier—Stokes and the Related Equations -- 1. Introduction -- 2. Littlewood—Paley decomposition -- 3. Proof of Theorems -- References -- The Commutation Error of the Space Averaged Navier—Stokes Equations on a Bounded Domain -- 1. Introduction -- 2. The space averaged Navier-Stokes equations in a bounded domain -- 3. The Gaussian filter -- 4. Error estimates in the (Lp(?d))d—norm of the commutation error term -- 5. Error estimates in the (H-1(?))d—norm of the commutation error term -- 6. Error estimates for a weak form of the commutation error term -- 7. The boundedness of the kinetic energy for ñ in some LES models -- References -- The Nonstationary Stokes and Navier—Stokes Flows Through an Aperture -- 1. Introduction -- 2. Results -- 3. The Stokes resolvent for the half space -- 4. The Stokes resolvent -- 5. L4-Lr estimates of the Stokes semigroup -- 6. The Navier—Stokes flow -- References -- Asymptotic Behavior at Infinity of Exterior Three-dimensional Steady Compressible Flow -- 1. Introduction -- 2. Function spaces and auxiliary results -- 3. Stokes and modified Stokes problems in weighted spaces -- 4. Transport equation and Poisson-type equation -- 5. Linearized problem -- 6. Nonlinear problem -- References 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 HTTP:URL=https://doi.org/10.1007/978-3-0348-7877-7

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