Keywords:
Global analysis (Mathematics).
;
Vector fields.
;
Differential equations, Partial.
;
Manifolds.
;
Fluid dynamics.
;
Geophysics.
;
Electronic books.
Type of Medium:
Online Resource
Pages:
1 online resource (248 pages)
Edition:
1st ed.
ISBN:
9781470413460
Series Statement:
Mathematical Surveys and Monographs ; v.119
URL:
https://ebookcentral.proquest.com/lib/geomar/detail.action?docID=3112720
DDC:
532/.0535
Language:
English
Note:
Intro -- Contents -- Preface -- Introduction -- 0.1. Representation of Fluid Flows -- 0.2. Motivation and Main Objectives -- 0.3. The User's Guide -- Notes for Introduction -- Chapter 1. Structure Classification of Divergence-Free Vector Fields -- 1.1. Limit Set Theorem -- 1.2. Poincare-Hopf Index Theorem on Manifolds with Boundaries -- 1.3. Structural Classification -- 1.4. Topological Classification -- Notes for Chapter 1 -- Chapter 2. Structural Stability of Divergence-Free Vector Fields -- 2.1. Structural Stability of Divergence-Free Vector Fields with Free Boundary Conditions -- 2.2. Structural Stability for Divergence-Free Vector Fields with Dirichlet Boundary Conditions -- 2.3. Two Dimensional Hamiltonian Structural Stability -- 2.4. Block Structure of Hamiltonian Vector Fields -- 2.5. Local Structural Stability -- Notes for Chapter 2 -- Chapter 3. Block Stability of Divergence-Free Vector Fields on Manifolds with Nonzero Genus -- 3.1. Instability on Manifolds with Nonzero Genus -- 3.2. Block Structure and Block Stability -- 3.3. Structural Evolution of the Taylor Vortices -- Notes for Chapter 3 -- Chapter 4. Structural Stability of Solutions of Navier-Stokes Equations -- 4.1. Genericity of Stable Steady States -- 4.2. Properties for Structurally Stable Solutions on the Reynolds Numbers -- 4.3. Asymptotic Hamiltonian Structural Stability -- 4.4. Asymptotic Block Stability -- 4.5. Periodic Structure of Solutions of the Navier-Stokes Equations -- 4.6. Structure of Solutions of the Rayleigh-Benard Convection -- Notes for Chapter 4 -- Chapter 5. Structural Bifurcation for One-Parameter Families of Divergence-Free Vector Fields -- 5.1. Necessary Conditions for Structural Bifurcation -- 5.2. Structural Bifurcation for Flows with No-Normal Flow Boundary Conditions -- 5.3. Structural Bifurcation for Flows with Dirichlet Boundary Conditions.
,
5.4. Boundary Layer Separations of Incompressible Flows I -- 5.5. Boundary Layer Separations of Incompressible Flows II -- 5.6. Structural Bifurcation near Interior Singular Points -- 5.7. Genericity of Structural Bifurcations -- Notes for Chapter 5 -- Chapter 6. Two Examples -- 6.1. Fluid Flow Maps and Double-Gyre Ocean Circulation -- 6.2. Boundary Layer Separation on Driven Cavity Flow -- Notes for Chapter 6 -- Bibliography -- Index -- A -- B -- C -- D -- E -- F -- G -- H -- I -- K -- L -- N -- O -- P -- Q -- R -- S -- T -- V.
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