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Mathematical Study of Degenerate Boundary Layers.
This paper is concerned with a complete asymptotic analysis as E \to 0 of the Munk equation \partial _x\psi -E \Delta ^2 \psi = \tau in a domain \Omega \subset \mathbf R^2, supplemented with boundary conditions for \psi and \partial _n \psi . This equation is a simple model for the circulation of cu...
| Clasificación: | Libro Electrónico |
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| Autor principal: | |
| Otros Autores: | |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Providence :
American Mathematical Society,
2018.
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| Colección: | Memoirs of the American Mathematical Society Ser.
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| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Title page; Chapter 1. Introduction; 1.1. Munk boundary layers; 1.1.1. State of the art; 1.1.2. Boundary layer degeneracies; 1.1.3. Stability of the stationary Munk equation; 1.2. Geometrical preliminaries; 1.2.1. Regularity and flatness assumptions; 1.2.2. Singularity lines; 1.2.3. Domains with islands; 1.2.4. Periodic domains and domains with corners; 1.3. Main approximation results; 1.3.1. General case; 1.3.2. Periodic and rectangle cases; 1.3.3. Outline of the paper; Chapter 2. Multiscale analysis; 2.1. Local coordinates and the boundary layer equation.
- 2.2. East and West boundary layers2.2.1. The scaled equation; 2.2.2. Domain of validity; 2.3. North and South boundary layers; 2.3.1. The scaled equation; 2.3.2. Study of the boundary layer equation (2.11):; 2.3.3. Boundary conditions for ∈( ᵢ, ᵢ₊₁); 2.3.4. Connection with East and West boundary layers; 2.4. Discontinuity zones; 2.4.1. Lifting the discontinuity; 2.4.2. The interior singular layer; 2.5. The case of islands; 2.6. North and South periodic boundary layers; Chapter 3. Construction of the approximate solution; 3.1. The interior term; 3.2. Lifting the East boundary conditions
- 4.1. Remainders stemming from the interior term ^{ }= ⁰_{ }+\psil4.1.1. Error terms due to the truncation _{\viscosite}.; 4.1.2. Error terms due to the lifting term \psil; 4.2. Remainders coming from the boundary terms; 4.2.1. Laplacian in curvilinear coordinates; 4.2.2. Error terms associated with North and South layers; 4.2.3. Error terms associated with East and West boundary layers; 4.2.4. Error terms associated with discontinuity layers; 4.3. Remainders in the periodic and rectangular cases; Chapter 5. Discussion: Physical relevance of the model; Acknowledgments; Appendix.
- Appendix A: The case of islands: derivation of the compatibility condition (1.15) and proof of Lemma 1.2.1Appendix B: Equivalents for the coordinates of boundary points near horizontal parts; Appendix C: Estimates on the coefficients and .; Appendix D: Proof of Lemma 3.4.3; Notations; Sizes of parameters and terms; Bibliography; Back Cover.