{"product_id":"9783764371043","title":"Advances in Mathematical Fluid Mechanics","description":"\u003ch1\u003eAdvances in Mathematical Fluid Mechanics\u003c\/h1\u003e \u003ch2\u003eGaldi, Giovanni P.; Heywood, John G.; Rannacher, Rolf\u003c\/h2\u003e \u003cp\u003eThis 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 \u0026lt; 5\/4.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Birkhäuser\u003c\/p\u003e \u003cp\u003ePublication Date: 2004-07-23\u003c\/p\u003e \u003cp\u003eFormat: Hardcover\u003c\/p\u003e \u003cp\u003eISBN-13: 9783764371043\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-0348-7877-7\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 152\u003c\/p\u003e ","brand":"Birkhäuser Basel","offers":[{"title":"Default Title","offer_id":46312187822220,"sku":"9783764371043","price":49.49,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783764371043.jpg?v=1771521185","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783764371043","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}