Advances in Mathematical Fluid Mechanics: Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999
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| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin, Heidelberg
Springer Berlin Heidelberg
2000
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| Online-Zugang: | Volltext |
| Beschreibung: | This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone addresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equations for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equations for compressible fluids. The global (in time) analysis of two and threedimensional motions of compressible fluids were left open for many years |
| Beschreibung: | 1 Online-Ressource (IX, 236p) |
| ISBN: | 9783642573088 9783540677864 |
| DOI: | 10.1007/978-3-642-57308-8 |
Internformat
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| 245 | 1 | 0 | |a Advances in Mathematical Fluid Mechanics |b Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 |c edited by Josef Málek, Jindřich Nečas, Mirko Rokyta |
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| 500 | |a This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone addresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equations for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equations for compressible fluids. The global (in time) analysis of two and threedimensional motions of compressible fluids were left open for many years | ||
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Datensatz im Suchindex
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| author2 | Málek, Josef Nečas, Jindřich Rokyta, Mirko |
| author2_role | edt edt edt |
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| author_facet | Málek, Josef Nečas, Jindřich Rokyta, Mirko |
| building | Verbundindex |
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| collection | ZDB-2-SMA ZDB-2-BAE |
| ctrlnum | (OCoLC)863669985 (DE-599)BVBBV042422672 |
| dewey-full | 515 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 515 - Analysis |
| dewey-raw | 515 |
| dewey-search | 515 |
| dewey-sort | 3515 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| doi_str_mv | 10.1007/978-3-642-57308-8 |
| format | Electronic eBook |
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| spelling | Málek, Josef edt Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 edited by Josef Málek, Jindřich Nečas, Mirko Rokyta Berlin, Heidelberg Springer Berlin Heidelberg 2000 1 Online-Ressource (IX, 236p) txt rdacontent c rdamedia cr rdacarrier This book consists of six survey contributions that are focused on several open problems of theoretical fluid mechanics both for incompressible and compressible fluids. The first article "Viscous flows in Besov spaces" by M area Cannone addresses the problem of global existence of a uniquely defined solution to the three-dimensional Navier-Stokes equations for incompressible fluids. Among others the following topics are intensively treated in this contribution: (i) the systematic description of the spaces of initial conditions for which there exists a unique local (in time) solution or a unique global solution for small data, (ii) the existence of forward self-similar solutions, (iii) the relation of these results to Leray's weak solutions and backward self-similar solutions, (iv) the extension of the results to further nonlinear evolutionary problems. Particular attention is paid to the critical spaces that are invariant under the self-similar transform. For sufficiently small Reynolds numbers, the conditional stability in the sense of Lyapunov is also studied. The article is endowed by interesting personal and historical comments and an exhaustive bibliography that gives the reader a complete picture about available literature. The papers "The dynamical system approach to the Navier-Stokes equations for compressible fluids" by Eduard Feireisl, and "Asymptotic problems and compressible-incompressible limits" by Nader Masmoudi are devoted to the global (in time) properties of solutions to the Navier-Stokes equations for compressible fluids. The global (in time) analysis of two and threedimensional motions of compressible fluids were left open for many years Mathematics Global analysis (Mathematics) Numerical analysis Mechanics, applied Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Fluid- and Aerodynamics Theoretical and Applied Mechanics Mathematik Strömungsmechanik (DE-588)4077970-1 gnd rswk-swf Numerisches Verfahren (DE-588)4128130-5 gnd rswk-swf 1\p (DE-588)1071861417 Konferenzschrift 1999 Paseky Mohelnice gnd-content Strömungsmechanik (DE-588)4077970-1 s Numerisches Verfahren (DE-588)4128130-5 s 2\p DE-604 Nečas, Jindřich edt Rokyta, Mirko edt https://doi.org/10.1007/978-3-642-57308-8 Verlag Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 Mathematics Global analysis (Mathematics) Numerical analysis Mechanics, applied Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Fluid- and Aerodynamics Theoretical and Applied Mechanics Mathematik Strömungsmechanik (DE-588)4077970-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| subject_GND | (DE-588)4077970-1 (DE-588)4128130-5 (DE-588)1071861417 |
| title | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 |
| title_auth | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 |
| title_exact_search | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 |
| title_full | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 edited by Josef Málek, Jindřich Nečas, Mirko Rokyta |
| title_fullStr | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 edited by Josef Málek, Jindřich Nečas, Mirko Rokyta |
| title_full_unstemmed | Advances in Mathematical Fluid Mechanics Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 edited by Josef Málek, Jindřich Nečas, Mirko Rokyta |
| title_short | Advances in Mathematical Fluid Mechanics |
| title_sort | advances in mathematical fluid mechanics lecture notes of the sixth international school mathematical theory in fluid mechanics paseky czech republic sept 19 26 1999 |
| title_sub | Lecture Notes of the Sixth International School Mathematical Theory in Fluid Mechanics, Paseky, Czech Republic, Sept. 19–26, 1999 |
| topic | Mathematics Global analysis (Mathematics) Numerical analysis Mechanics, applied Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Fluid- and Aerodynamics Theoretical and Applied Mechanics Mathematik Strömungsmechanik (DE-588)4077970-1 gnd Numerisches Verfahren (DE-588)4128130-5 gnd |
| topic_facet | Mathematics Global analysis (Mathematics) Numerical analysis Mechanics, applied Analysis Numerical Analysis Theoretical, Mathematical and Computational Physics Fluid- and Aerodynamics Theoretical and Applied Mechanics Mathematik Strömungsmechanik Numerisches Verfahren Konferenzschrift 1999 Paseky Mohelnice |
| url | https://doi.org/10.1007/978-3-642-57308-8 |
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