Contributions to Current Challenges in Mathematical Fluid Mechanics
Başlık:
Contributions to Current Challenges in Mathematical Fluid Mechanics
ISBN:
9783034878777
Edition:
1st ed. 2004.
Yayın Bilgileri:
Basel : Birkhäuser Basel : Imprint: Birkhäuser, 2004.
Fiziksel Tanımlama:
VIII, 152 p. online resource.
Series:
Advances in Mathematical Fluid Mechanics,
Contents:
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.
Abstract:
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.
Ek Kurum Yazarı:
Dil:
English