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OverviewThe 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. Full Product DetailsAuthor: Jean-Yves Chemin (Professor, Professor, University of Paris VI and Institut Universitaire de France) , Isabelle Gallagher , Dragos Iftimie (, both at University of Paris VI, France)Publisher: Oxford University Press Imprint: Oxford University Press Volume: 14 Dimensions: Width: 16.10cm , Height: 1.60cm , Length: 24.20cm Weight: 0.450kg ISBN: 9780198503972ISBN 10: 0198503970 Pages: 198 Publication Date: 10 September 1998 Audience: Professional and scholarly , Professional & Vocational Format: Hardback Publisher's Status: Active Availability: To order  Stock availability from the supplier is unknown. We will order it for you and ship this item to you once it is received by us. Table of ContentsIntroduction 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 ReferencesReviewsAuthor InformationTab Content 6Author Website:Countries AvailableAll regions |
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