Contributions to Current Challenges in Mathematical Fluid Mechanics / edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher
(Advances in Mathematical Fluid Mechanics)
| データ種別 | 電子ブック |
|---|---|
| 出版情報 | Basel : Birkhäuser Basel : Imprint: Birkhäuser , 2004 |
| 本文言語 | 英語 |
| 大きさ | VIII, 152 p : online resource |
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| 内容注記 | 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 |
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| 一般注記 | 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 |
| 著者標目 | Galdi, Giovanni P. editor Heywood, John G. editor Rannacher, Rolf editor SpringerLink (Online service) |
| 件 名 | LCSH:Physics LCSH:Partial differential equations LCSH:Continuum physics FREE:Physics FREE:Classical Continuum Physics FREE:Partial Differential Equations FREE:Mathematical Methods in Physics |
| 分 類 | DC23:531 |
| 巻冊次 | ISBN:9783034878777 
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| ISBN | 9783034878777 |
| URL | http://dx.doi.org/10.1007/978-3-0348-7877-7 |
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