{"product_id":"perfect-incompressible-fluids","title":"Perfect Incompressible Fluids","description":"\u003cp\u003eThe 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\n\u003cbr\u003enecessary 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\n\u003cbr\u003econcerning 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.\u003c\/p\u003e","brand":"Oxford University Press","offers":[{"title":"Default Title","offer_id":46058392649966,"sku":"9780198503972","price":391.1,"currency_code":"AUD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0630\/9612\/7726\/files\/9780198503972.jpg?v=1736474907","url":"https:\/\/bookland.com.au\/products\/perfect-incompressible-fluids","provider":"Book Land AU","version":"1.0","type":"link"}