Title: Perfect Incompressible Fluids (Oxford Lecture Series in Mathematics and Its Applications)
Publisher: Clarendon Press
Publication Date: 1998
Language: English
ISBN 10: 0198503970
ISBN 13: 9780198503972
Binding: Hardcover
Condition: New

About this title

Synopsis

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 analysis: 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.

About the Author

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

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