Buch, Englisch, 198 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 467 g
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Buch, Englisch, 198 Seiten, Print PDF, Format (B × H): 161 mm x 240 mm, Gewicht: 467 g
ISBN: 978-0-19-850397-2
Verlag: ACADEMIC
The aim of this book is to offer a direct and self-contained access to some of the new or recent results in fluid mechanics. It gives an authoritative account on the theory of the Euler equations describing a perfect incompressible fluid. First of all, the text derives the Euler equations from a variational principle, and recalls the relations on vorticity and pressure. Various weak formulations are proposed. The book then presents the tools of analysis necessary for their study: Littlewood-Paley theory, action of Fourier multipliers on L spaces, and partial differential calculus. These techniques are then used to prove various recent results concerning vortext patches or sheets, essentially the persistence of the smoothness of the boundary of a vortex patch, even if that smoothness allows singular points, as well as the existence of weak solutions of the vorticity sheet type. The text also presents properties of microlocal (analytic or Gevrey) regularity of the solutions of Euler equations, and provides links of such properties to the smoothness in time of the flow of the solution vector field.
Fachgebiete
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Computeranwendungen in der Mathematik
- Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
- Naturwissenschaften Physik Thermodynamik Festkörperphysik, Kondensierte Materie
- Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Strömungslehre
- Naturwissenschaften Physik Mechanik Kontinuumsmechanik, Strömungslehre
- Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
Weitere Infos & Material
- Introduction
- 1: Presentation of the equations
- 2: Littlewood-Paley theory
- 3: Around Biot-Savart's law
- 4: The case of a smooth initial data
- 5: When the vorticity is bounded
- 6: Vortex sheets
- 7: The wave front and the product
- 8: Analyticity and Gevrey regularity
- 9: Singular vortex patches
- References
