Perfect incompressible fluids
著者
書誌事項
Perfect incompressible fluids
（Oxford lecture series in mathematics and its applications, 14）
Clarendon Press , Oxford University Press, 1998
- タイトル別名
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Fluides parfaits incompressibles
- 統一タイトル
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Fluides parfaits incompressibles
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注記
Includes bibliographical references (p.181-185) and index
内容説明・目次
内容説明
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.
目次
- 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
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