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Perfect Incompressible Fluids by Jean-Yves Chemin, Dragos Iftimie, Isabelle Gallagher

Perfect Incompressible Fluids

by Jean-Yves Chemin , Dragos Iftimie , Isabelle Gallagher
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Book cover type: Hardcover
  • ISBN13: 9780198503972
  • Binding: Hardcover
  • Subject: N/A
  • Publisher: Clarendon Press
  • Publisher Imprint: Clarendon Press
  • Publication Date:
  • Pages: 200
  • Original Price: USD 230.0
  • Language: English
  • Edition: N/A
  • Item Weight: 431 grams
  • BISAC Subject(s): Differential Equations / Partial

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.

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