Perfect Incompressible Fluids

Hardcover | August 1, 1998

byJean-Yves CheminTranslated byIsabelle Gallagher, Dragos Iftimie

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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 equationsfrom 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 differentialcalculus. 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 thevorticity 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.

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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 equationsfrom a variational principle, and recalls the ...

Jean-Yves Chemin is at University of Paris VI and Institut Universitaire de France. Dragos Iftimie is at both at University of Paris VI.

other books by Jean-Yves Chemin

Format:HardcoverDimensions:198 pages, 9.21 × 6.14 × 0.63 inPublished:August 1, 1998Publisher:Oxford University Press

The following ISBNs are associated with this title:

ISBN - 10:0198503970

ISBN - 13:9780198503972

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Table of Contents

Introduction1. Presentation of the equations2. Littlewood-Paley theory3. Around Biot-Savart's law4. The case of a smooth initial data5. When the vorticity is bounded6. Vortex sheets7. The wave front and the product8. Analyticity and Gevrey regularity9. Singular vortex patchesReferences