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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 |
MARC
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| 003 | OCoLC | ||
| 005 | 20240329122006.0 | ||
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| 020 | |a 9781470444075 | ||
| 020 | |a 1470444070 | ||
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| 049 | |a UAMI | ||
| 100 | 1 | |a Dalibard, Anne-Laure. | |
| 245 | 1 | 0 | |a Mathematical Study of Degenerate Boundary Layers. |
| 260 | |a Providence : |b American Mathematical Society, |c 2018. | ||
| 300 | |a 1 online resource (118 pages) | ||
| 336 | |a text |b txt |2 rdacontent | ||
| 337 | |a computer |b c |2 rdamedia | ||
| 338 | |a online resource |b cr |2 rdacarrier | ||
| 490 | 1 | |a Memoirs of the American Mathematical Society Ser. ; |v v. 253 | |
| 588 | 0 | |a Print version record. | |
| 505 | 0 | |6 880-01 |a 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. | |
| 505 | 8 | |a 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 | |
| 505 | 8 | |a 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. | |
| 505 | 8 | |a 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. | |
| 520 | |a 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 currents in closed basins, the variables x and y being respectively the longitude and the latitude. A crude analysis shows that as E \to 0, the weak limit of \psi satisfies the so-called Sverdrup transport equation inside the domain, namely \partial _x \psi ^0=\tau, while boundary layers appear in. | ||
| 590 | |a ProQuest Ebook Central |b Ebook Central Academic Complete | ||
| 650 | 0 | |a Boundary layer. | |
| 650 | 0 | |a Ocean currents |x Mathematical models. | |
| 650 | 0 | |a Ocean circulation |x Mathematical models. | |
| 650 | 6 | |a Couche limite. | |
| 650 | 6 | |a Courants marins |x Modèles mathématiques. | |
| 650 | 6 | |a Circulation océanique |x Modèles mathématiques. | |
| 650 | 7 | |a Boundary layer |2 fast | |
| 650 | 7 | |a Ocean circulation |x Mathematical models |2 fast | |
| 650 | 7 | |a Ocean currents |x Mathematical models |2 fast | |
| 700 | 1 | |a Saint-Raymond, Laure. | |
| 758 | |i has work: |a Mathematical study of degenerate boundary layers (Text) |1 https://id.oclc.org/worldcat/entity/E39PCGV7FPPv7pXhvXMXGq6yv3 |4 https://id.oclc.org/worldcat/ontology/hasWork | ||
| 776 | 0 | 8 | |i Print version: |a Dalibard, Anne-Laure. |t Mathematical Study of Degenerate Boundary Layers: a Large Scale Ocean Circulation Problem. |d Providence : American Mathematical Society, ©2018 |z 9781470428358 |
| 830 | 0 | |a Memoirs of the American Mathematical Society Ser. | |
| 856 | 4 | 0 | |u https://ebookcentral.uam.elogim.com/lib/uam-ebooks/detail.action?docID=5409174 |z Texto completo |
| 880 | 8 | |6 505-01/(S |a 3.2.1. Traces of the East boundary layers3.2.2. Definition of the East corrector; 3.3. North and South boundary layers; 3.3.1. Definition of the initial boundary value problem; 3.3.2. Estimates for _{, }; 3.3.3. Extinction and truncation; 3.4. The interface layer; 3.4.1. The lifting term \psil; 3.4.2. The interior singular layer ^{Σ}; 3.4.3. Connection with the West boundary; 3.5. Lifting the West boundary conditions; 3.6. Approximate solution in the periodic and rectangle case; 3.6.1. In the periodic case; 3.6.2. In the rectangle case; Chapter 4. Proof of convergence. | |
| 938 | |a EBL - Ebook Library |b EBLB |n EBL5409174 | ||
| 994 | |a 92 |b IZTAP | ||