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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Jean-Yves Chemin is at University of Paris VI and Institut Universitaire de France. Dragos Iftimie is at both at University of Paris VI.Language Notes:
Text: English (translation)
Original Language: French
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Book Description Oxford University Press, USA, 1998. Hardcover. Book Condition: New. Bookseller Inventory # DADAX0198503970
Book Description Clarendon Press, 1998. Hardcover. Book Condition: New. Never used!. Bookseller Inventory # P110198503970
Book Description Clarendon Press, 1998. Hardcover. Book Condition: New. book. Bookseller Inventory # M0198503970
Book Description Oxford Univ Pr, 1998. Hardcover. Book Condition: Brand New. 1st edition. 200 pages. 9.75x6.50x0.50 inches. In Stock. Bookseller Inventory # 0198503970