Dewey Class 
531 
Title 
Contributions to Current Challenges in Mathematical Fluid Mechanics ([EBook]) / edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher. 
Added Personal Name 
Galdi, Giovanni Paolo , 1947 
Heywood, John G. 
Rannacher, Rolf 
Other name(s) 
SpringerLink (Online service) 
Publication 
Basel : Birkhäuser , 2004. 
Physical Details 
VIII, 152 pages : online resource. 
Series 
Advances in mathematical fluid mechanics 
ISBN 
9783034878777 
Summary Note 
This volume consists of five research articles, each dedicated to a significant topic in the mathematical theory of the NavierStokes 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 socalled Kolmogorovobukhov fivethirds 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 multidimensional 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 KolmogorovObukhov law are discussed. Similar estimates are also obtained for the NavierStokes 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 NavierStokes equations at high Reynolds numbers. The paper of of D. Chae and J. Lee investigates the global wellposedness 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.: 
Contents note 
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 Wellposedness 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 NavierStokes 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 (H1(?))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. L4Lr estimates of the Stokes semigroup  6. The Navier—Stokes flow  References  Asymptotic Behavior at Infinity of Exterior Threedimensional Steady Compressible Flow  1. Introduction  2. Function spaces and auxiliary results  3. Stokes and modified Stokes problems in weighted spaces  4. Transport equation and Poissontype equation  5. Linearized problem  6. Nonlinear problem  References. 
System details note 
Online access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users) 
Internet Site 
http://dx.doi.org/10.1007/9783034878777 
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