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Mathematical aspects of fluid mechanics /
The rigorous mathematical theory of the equations of fluid dynamics has been a focus of intense activity in recent years. This volume is the product of a workshop held at the University of Warwick to consolidate, survey and further advance the subject. The Navier-Stokes equations feature prominently...
| Clasificación: | Libro Electrónico |
|---|---|
| Otros Autores: | , , |
| Formato: | Electrónico eBook |
| Idioma: | Inglés |
| Publicado: |
Cambridge, UK :
Cambridge University Press,
©2012.
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| Colección: | London Mathematical Society lecture note series ;
402. |
| Temas: | |
| Acceso en línea: | Texto completo |
Tabla de Contenidos:
- Cover; LONDON MATHEMATICAL SOCIETY LECTURE NOTE SERIES; Title; Copyright; Dedication; Contents; Contents; Preface; Preface; List of Contributors; List of Contributors; 1 Towards fluid equations by approximate deconvolution models; 1.1 Introduction; 1.2 The approximate deconvolution; 1.3 High accuracy deconvolution alpha-models; 1.4 Energy spectrum; 1.5 Limiting behaviour in terms of the deconvolution parameter; References; 2 On flows of fluids described by an implicit constitutive equation characterized by a maximal monotone graph; 2.1 Introduction; 2.2 Orlicz spaces; 2.3 Selections.
- 2.4 Convergence tools2.5 Steady flows without convection; 2.6 Steady flows with convection; 2.7 Unsteady flows without convection; 2.8 Full problem; Acknowledgments; References; 3 A continuous model for turbulent energy cascade; 3.1 Motivation for the model; 3.1.1 Onsager and Kolmogorov; 3.1.2 Onsager's Conjecture and Besov spaces; 3.1.3 Littlewood-Paley framework for intermittency; 3.2 A continuous model for the energy flux; 3.3 Inviscid case; 3.4 Viscous case; References; 4 Remarks on complex fluid models; 4.1 Introduction; 4.2 Energetics; 4.3 Global existence issues; 4.4 Uniqueness issues.
- 7.2.3 Stabilization via a control supported on part of the boundary7.3 Construction of a stabilizing control for the Oseen equations; 7.3.1 Reduction to the linear case; 7.3.2 Description of the "correct" initial conditions; 7.3.3 Theorem on the stabilization of the Oseen equations; 7.4 Stabilization for the Navier-Stokes equations; 7.4.1 Definition of the stable invariant manifold; 7.4.2 Feedback operator and stabilization; 7.5 Feedback property for a control; 7.5.1 Definitions. The case of initial control; 7.5.2 The case of distributed control supported in a subdomain; 7.5.3 Real processes.
- 7.6 Description of numerical algorithms7.6.1 General definitions; 7.6.2 Stable invariant manifold for a fixed point; 7.6.3 Projection onto the stable invariant manifold; 7.6.4 The stable manifold corresponding to a trajectory; 7.6.5 Projection onto the stable manifold; 7.6.6 Calculations with control in the right-hand side; 7.7 Results of numerical calculations; 7.7.1 The physical model and its mathematical setting; 7.7.2 The structure of the phase portrait; 7.7.3 Stabilization by control of the initial condition; 7.7.4 Stabilization by control of the right-hand side.