Geometric theory of incompressible flows with applications to fluid dynamics:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Providence, RI
American Mathematical Society
2005
|
| Series: | Mathematical surveys and monographs
119 |
| Subjects: | |
| Links: | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017328253&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| Item Description: | Includes bibliographical references (p. 229-232) and index |
| Physical Description: | IX, 234 S. Ill. |
| ISBN: | 0821836935 |
Staff View
MARC
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| 245 | 1 | 0 | |a Geometric theory of incompressible flows with applications to fluid dynamics |c Tian Ma ; Shouhong Wang |
| 264 | 1 | |a Providence, RI |b American Mathematical Society |c 2005 | |
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| 650 | 7 | |a Mecânica dos fluídos |2 larpcal | |
| 650 | 4 | |a Global analysis (Mathematics) | |
| 650 | 4 | |a Vector fields | |
| 650 | 4 | |a Differential equations, Partial | |
| 650 | 4 | |a Manifolds | |
| 650 | 4 | |a Fluid dynamics | |
| 650 | 4 | |a Geophysics | |
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Record in the Search Index
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|---|---|
| adam_text | Contents
Preface ix
Introduction 1
0.1. Representation of Fluid Flows 1
0.2. Motivation and Main Objectives 2
0.3. The User s Guide 4
Notes for Introduction 14
Chapter 1. Structure Classification of Divergence-Free Vector Fields 17
1.1. Limit Set Theorem 17
1.2. Poincare-Hopf Index Theorem on Manifolds with Boundaries 24
1.3. Structural Classification 31
1.4. Topological Classification 40
Notes for Chapter 1 49
Chapter 2. Structural Stability of Divergence-Free Vector Fields 51
2.1. Structural Stability of Divergence-Free Vector Fields with Free
Boundary Conditions 51
2.2. Structural Stability for Divergence-Free Vector Fields with Dirichlet
Boundary Conditions 60
2.3. Two Dimensional Hamiltonian Structural Stability 71
2.4. Block Structure of Hamiltonian Vector Fields 75
2.5. Local Structural Stability 77
Notes for Chapter 2 80
Chapter 3. Block Stability of Divergence-Free Vector Fields on Manifolds
with Nonzero Genus 81
3.1. Instability on Manifolds with Nonzero Genus 81
3.2. Block Structure and Block Stability 87
3.3. Structural Evolution of the Taylor Vortices 98
Notes for Chapter 3 108
Chapter 4. Structural Stability of Solutions of Navier-Stokes Equations 109
4.1. Genericity of Stable Steady States 109
4.2. Properties for Structurally Stable Solutions on the Reynolds Numbers 114
4.3. Asymptotic Hamiltonian Structural Stability 117
4.4. Asymptotic Block Stability 123
4.5. Periodic Structure of Solutions of the Navier-Stokes Equations 127
4.6. Structure of Solutions of the Rayleigh-Benard Convection 142
Notes for Chapter 4 155
vii
viii CONTENTS
Chapter 5. Structural Bifurcation for One-Parameter Families of Divergence-
Free Vector Fields 157
5.1. Necessary Conditions for Structural Bifurcation 157
5.2. Structural Bifurcation for Flows with No-Normal Flow Boundary
Conditions 160
5.3. Structural Bifurcation for Flows with Dirichlet Boundary Conditions 167
5.4. Boundary Layer Separations of Incompressible Flows I 177
5.5. Boundary Layer Separations of Incompressible Flows II 181
5.6. Structural Bifurcation near Interior Singular Points 187
5.7. Genericity of Structural Bifurcations 198
Notes for Chapter 5 201
Chapter 6. Two Examples 203
6.1. Fluid Flow Maps and Double-Gyre Ocean Circulation 203
6.2. Boundary Layer Separation on Driven Cavity Flow 210
Notes for Chapter 6 221
Bibliography 229
Index 233
|
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| id | DE-604.BV035407706 |
| illustrated | Illustrated |
| indexdate | 2024-12-20T13:31:48Z |
| institution | BVB |
| isbn | 0821836935 |
| language | English |
| lccn | 2005048120 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-017328253 |
| oclc_num | 60402155 |
| open_access_boolean | |
| owner | DE-29T DE-188 |
| owner_facet | DE-29T DE-188 |
| physical | IX, 234 S. Ill. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | American Mathematical Society |
| record_format | marc |
| series | Mathematical surveys and monographs |
| series2 | Mathematical surveys and monographs |
| spellingShingle | Ma, Tian 1956- Geometric theory of incompressible flows with applications to fluid dynamics Mathematical surveys and monographs Equações de navier-stokes larpcal Equações diferenciais parciais (análise) larpcal Mecânica dos fluídos larpcal Global analysis (Mathematics) Vector fields Differential equations, Partial Manifolds Fluid dynamics Geophysics Inkompressible Strömung (DE-588)4129759-3 gnd Geometrisches Modell (DE-588)4452959-4 gnd |
| subject_GND | (DE-588)4129759-3 (DE-588)4452959-4 |
| title | Geometric theory of incompressible flows with applications to fluid dynamics |
| title_auth | Geometric theory of incompressible flows with applications to fluid dynamics |
| title_exact_search | Geometric theory of incompressible flows with applications to fluid dynamics |
| title_full | Geometric theory of incompressible flows with applications to fluid dynamics Tian Ma ; Shouhong Wang |
| title_fullStr | Geometric theory of incompressible flows with applications to fluid dynamics Tian Ma ; Shouhong Wang |
| title_full_unstemmed | Geometric theory of incompressible flows with applications to fluid dynamics Tian Ma ; Shouhong Wang |
| title_short | Geometric theory of incompressible flows with applications to fluid dynamics |
| title_sort | geometric theory of incompressible flows with applications to fluid dynamics |
| topic | Equações de navier-stokes larpcal Equações diferenciais parciais (análise) larpcal Mecânica dos fluídos larpcal Global analysis (Mathematics) Vector fields Differential equations, Partial Manifolds Fluid dynamics Geophysics Inkompressible Strömung (DE-588)4129759-3 gnd Geometrisches Modell (DE-588)4452959-4 gnd |
| topic_facet | Equações de navier-stokes Equações diferenciais parciais (análise) Mecânica dos fluídos Global analysis (Mathematics) Vector fields Differential equations, Partial Manifolds Fluid dynamics Geophysics Inkompressible Strömung Geometrisches Modell |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017328253&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000018014 |
| work_keys_str_mv | AT matian geometrictheoryofincompressibleflowswithapplicationstofluiddynamics AT wangshouhong geometrictheoryofincompressibleflowswithapplicationstofluiddynamics |