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Partial differential equations in fluid mechanics /
A selection of survey articles and original research papers in mathematical fluid mechanics, for both researchers and graduate students.
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, United Kingdom :
Cambridge University Press,
2018.
|
| Colección: | London Mathematical Society lecture note series ;
452. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; Series information; Title page; Copyright information; Table of contents; List of contributors; Preface; 1 Remarks on recent advances concerning boundary effects and the vanishing viscosity limit of the Navier-Stokes equations; Abstract; 1.1 Introduction and uniform estimates; 1.2 Kato criterion for convergence to the regular solution; 1.3 Mathematical and physical interpretation of Theorem 1.3; 1.3.1 Recirculation; 1.3.2 The Prandtl equations and the Stewartson triple-deck ansatz; 1.3.3 Von Karman turbulent Layer; 1.3.4 Energy limit and d'Alembert paradox
- 1.4 Kato's criterion, anomalous energy dissipation, and turbulenceReferences; 2 Time-periodic flow of a viscous liquid past a body; Abstract; 2.1 Introduction; 2.2 Notation; 2.3 Preliminaries; 2.4 An Embedding Theorem; 2.5 Linearized Problem; 2.6 Fully Nonlinear Problem; Acknowledgements; References; 3 The Rayleigh-Taylor instability in buoyancy-driven variable density turbulence; Abstract; 3.1 Background to the Rayleigh-Taylor instability; 3.2 The 3D Cahn-Hilliard-Navier-Stokes equations; 3.3 The variable density model for two incompressible miscible fluids; 3.3.1 The mathematical model
- 5 Quasi-invariance for the Navier-Stokes equations5.1 Introduction; 5.2 Navier-Stokes equations; 5.3 Burgers equation; 5.4 Use of critical dependent variables; 5.5 Cole-Hopf transform and Feynman-Kac formula; 5.6 Dynamic scaling transform; 5.6.1 Change of probability measures; 5.6.2 Leray equations; 5.6.3 Navier-Stokes equations; 5.7 Summary; Appendix A Wiener process; References; 6 Leray's fundamental work on the Navier-Stokes equations: a modern review of "Sur le mouvement d'un liquide visqueux emplissant l'espace"; Abstract; 6.1 Introduction; 6.1.1 Preliminaries; 6.1.2 The Oseen kernel T
- 6.2 The Stokes equations6.2.1 A general forcing F; 6.2.2 A forcing of the form F = −(Y · ∇)Y; Notes; 6.3 Strong solutions of the Navier-Stokes equations; 6.3.1 Properties of strong solutions; 6.3.2 Local existence and uniqueness of strong solutions; 6.3.3 Characterisation of singularities; 6.3.4 Semi-strong solutions; Notes; 6.4 Weak solutions of the Navier-Stokes equations; 6.4.1 Well-posedness for the regularised equations; 6.4.2 Global existence of a weak solution; 6.4.3 Structure of the weak solution; Notes; Acknowledgements; 6.5 Appendix; 6.5.1 The heat equation and the heat kernel