Contributions to Current Challenges in Mathematical Fluid Mechanics:
Gespeichert in:
| Beteilige Person: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | Englisch |
| Veröffentlicht: |
Basel
Birkhäuser Basel
2004
|
| Schriftenreihe: | Advances in Mathematical Fluid Mechanics
|
| Schlagwörter: | |
| Links: | https://doi.org/10.1007/978-3-0348-7877-7 |
| Beschreibung: | 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 |
| Umfang: | 1 Online-Ressource (VIII, 152 p) |
| ISBN: | 9783034878777 9783034896061 |
| DOI: | 10.1007/978-3-0348-7877-7 |
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| 500 | |a 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 | ||
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Datensatz im Suchindex
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| author | Galdi, Giovanni P. |
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| format | Electronic eBook |
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| isbn | 9783034878777 9783034896061 |
| language | English |
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| publishDate | 2004 |
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| series2 | Advances in Mathematical Fluid Mechanics |
| spellingShingle | Galdi, Giovanni P. Contributions to Current Challenges in Mathematical Fluid Mechanics Physics Differential equations, partial Mathematical physics Classical Continuum Physics Partial Differential Equations Mathematical Methods in Physics Mathematische Physik Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| subject_GND | (DE-588)4041456-5 (DE-588)4077970-1 (DE-588)4143413-4 |
| title | Contributions to Current Challenges in Mathematical Fluid Mechanics |
| title_auth | Contributions to Current Challenges in Mathematical Fluid Mechanics |
| title_exact_search | Contributions to Current Challenges in Mathematical Fluid Mechanics |
| title_full | Contributions to Current Challenges in Mathematical Fluid Mechanics edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher |
| title_fullStr | Contributions to Current Challenges in Mathematical Fluid Mechanics edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher |
| title_full_unstemmed | Contributions to Current Challenges in Mathematical Fluid Mechanics edited by Giovanni P. Galdi, John G. Heywood, Rolf Rannacher |
| title_short | Contributions to Current Challenges in Mathematical Fluid Mechanics |
| title_sort | contributions to current challenges in mathematical fluid mechanics |
| topic | Physics Differential equations, partial Mathematical physics Classical Continuum Physics Partial Differential Equations Mathematical Methods in Physics Mathematische Physik Navier-Stokes-Gleichung (DE-588)4041456-5 gnd Strömungsmechanik (DE-588)4077970-1 gnd |
| topic_facet | Physics Differential equations, partial Mathematical physics Classical Continuum Physics Partial Differential Equations Mathematical Methods in Physics Mathematische Physik Navier-Stokes-Gleichung Strömungsmechanik Aufsatzsammlung |
| url | https://doi.org/10.1007/978-3-0348-7877-7 |
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