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Perfect Incompressible Fluids Synopsis

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.

Book Information

ISBN: 9780198503972
Publication date: 6th August 1998
Author: Jean-Yves (Professor, University of Paris VI and Institut Universitaire de France) Chemin
Publisher: Clarendon Press an imprint of Oxford University Press
Format: Hardback
Pagination: 198 pages
Categories: Fluid mechanics, Differential calculus & equations, Applied mathematics, Mechanics of fluids,

About Jean-Yves (Professor, University of Paris VI and Institut Universitaire de France) Chemin

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