{"product_id":"contributions-to-current-challenges-in-mathematical-fluid-mechanics-von-undefined","title":"Contributions to Current Challenges 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 \u0026lt; 5\/4.\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783764371043\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e\u003cdiv class=\"aw-variant-hidden-subtitle-div\" id=\"aw-variant-subtitle-9783034896061\"\u003e\u003ch3\u003e\u003c\/h3\u003e\u003c\/div\u003e","brand":"Autorenwelt Shop","offers":[{"title":"Hardcover - 9783764371043","offer_id":49593016058181,"sku":"9783764371043","price":53.49,"currency_code":"EUR","in_stock":true},{"title":"Softcover - 9783034896061","offer_id":49592319902021,"sku":"9783034896061","price":53.49,"currency_code":"EUR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0940\/0622\/files\/cac5fa40-1043-45ee-b3e7-74a581366835.jpg?v=1772083183","url":"https:\/\/shop.autorenwelt.de\/en\/products\/contributions-to-current-challenges-in-mathematical-fluid-mechanics-von-undefined","provider":"Autorenwelt Shop","version":"1.0","type":"link"}