Perfect Incompressible Fluids

by Jean-Yves Chemin, Isabelle Gallagher (Translator), Dragos Iftimie (Translator)

An accessible and self-contained introduction to recent advances in fluid dynamics, this book provides an authoritative account of the Euler equations for a perfect incompressible fluid. The book begins with a derivation of the Euler equations from a variational principle. It then recalls the relations on vorticity and pressure and proposes various weak formulations. The book develops the key tools for the Littlewood-Paley theory, action of Fourier multipliers on L spaces, and partial differential calculus. These techniques are used to prove various recent results concerning vortex patches or sheets; the main results include the persistence of the smoothness of the boundary of a vortex patch, even if that smoothness allows singular points, and 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 links such properties to the smoothness in
time of the flow of the solution vector field.

Hardcover

First published December 10, 1998

Reviews

[Jacob · Rating 3 out of 5]

A good (so far at least) introduction to fluid dynamics, though I think saying Chemin's proofs and arguments are terse and that his exposition is a bit opaque might be an understatement.

Also, it is translated verbatim from the French, so be prepared for some less than perfect sentence structure and some strange turns of phrase.

[Hamid]

Perfect Incompressible Fluids