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Contributions to Current Challenges in Mathematical Fluid Mechanics
Tag	Description
020	$a9783034878777
082	$a531
099	$aOnline resource : Birkhäuser
245	$aContributions to Current Challenges in Mathematical Fluid Mechanics$h[EBook]$cedited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher.
260	$aBasel$bBirkhäuser$c2004.
300	$aVIII, 152 pages$bonline resource.
336	$atext
338	$aonline resource
440	$aAdvances in Mathematical Fluid Mechanics
505	$aOn 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.
520	$aThis 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.
538	$aOnline access to this digital book is restricted to subscription institutions through IP address (only for SISSA internal users)
700	$aGaldi, Giovanni Paolo$d1947-$eeditor.
700	$aHeywood, John G.$eeditor.
700	$aRannacher, Rolf.$eeditor.
710	$aSpringerLink (Online service)
830	$aAdvances in Mathematical Fluid Mechanics
856	$uhttp://dx.doi.org/10.1007/978-3-0348-7877-7