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Perfect Incompressible Fluids by Jean-Yves (Professor, University of Paris VI and Institut Universitaire de France) Chemin
  

Synopsis

Perfect Incompressible Fluids by Jean-Yves (Professor, University of Paris VI and Institut Universitaire de France) Chemin

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.

About the Author

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Book Info

Publication date

6th August 1998

Author

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

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Publisher

Clarendon Press an imprint of Oxford University Press

Format

Hardback
198 pages

Categories

Fluid mechanics
Differential calculus & equations
Applied mathematics
Mechanics of fluids

ISBN

9780198503972

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