{"product_id":"9783034896061","title":"Contributions to Current Challenges in Mathematical Fluid Mechanics (Advances in Mathematical Fluid Mechanics)","description":"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. 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. The mathematical theory of the Navier-Stokes equations presents fundamental open questions that represent many challenges for the interested mathematicians. This volume contains a series of articles whose objective is to furnish new contributions and ideas to these questions, with particular regard to turbulence modelling, regularity of solutions to the initial-value problem, flow in region with an unbounded boundary, and compressible flow.\u003cbr\u003e","brand":"Springer, Basel; Birkh\u0026auml;user","offers":[{"title":"Default Title","offer_id":48771836182763,"sku":"00000_00000_00000_00000","price":100.69,"currency_code":"SGD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0758\/4484\/5803\/files\/9783034896061-1.jpg?v=1783558370","url":"https:\/\/kinokuniya.com.sg\/products\/9783034896061","provider":"Books Kinokuniya Singapore","version":"1.0","type":"link"}