{"product_id":"9783319801629","title":"Navier–Stokes Equations on R3 × [0, T]","description":"\u003ch1\u003eNavier–Stokes Equations on R3 × [0, T]\u003c\/h1\u003e \u003ch2\u003eStenger, Frank; Tucker, Don; Baumann, Gerd\u003c\/h2\u003e \u003cp\u003e\u003c\/p\u003e\u003cp\u003eIn this monograph, leading researchers in the world of\nnumerical analysis, partial differential equations, and hard computational\nproblems study the properties of solutions of the Navier–Stokes\u003cb\u003e \u003c\/b\u003epartial differential equations on (x, y, z,\nt) ∈ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e]. Initially converting the PDE to a\nsystem of integral equations, the authors then describe spaces \u003cb\u003eA\u003c\/b\u003e of analytic functions that house\nsolutions of this equation, and show that these spaces of analytic functions\nare dense in the spaces \u003ci\u003eS\u003c\/i\u003e of rapidly\ndecreasing and infinitely differentiable functions. This method benefits from\nthe following advantages:\u003c\/p\u003e\u003cul\u003e\n \u003cli\u003eThe functions of S are\n     nearly always conceptual rather than explicit\u003c\/li\u003e\n \u003cli\u003eInitial and boundary\n     conditions of solutions of PDE are usually drawn from the applied sciences,\n     and as such, they are nearly always piece-wise analytic, and in this case,\n     the solutions have the same properties\u003c\/li\u003e\n \u003cli\u003eWhen methods of\napproximation are applied to functions of \u003cb\u003eA\u003c\/b\u003e they converge at an exponential rate, whereas methods of\n     approximation applied to the functions of \u003cb\u003eS\u003c\/b\u003e converge only at a polynomial rate\u003c\/li\u003e\n \u003cli\u003eEnables sharper bounds on\n     the solution enabling easier existence proofs, and a more accurate and\n     more efficient method of solution, including accurate error bounds\u003c\/li\u003e\n\u003c\/ul\u003e\u003cp\u003e\n\n\n\n\u003c\/p\u003e\u003cp\u003eFollowing the proofs of denseness, the authors prove the\nexistence of a solution of the integral equations in the space of functions \u003cb\u003eA\u003c\/b\u003e ∩ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e], and provide an explicit novel\nalgorithm based on Sinc approximation and Picard–like iteration for computing\nthe solution. Additionally, the authors include appendices that provide a\ncustom Mathematica program for computing solutions based on the explicit\nalgorithmic approximation procedure, and which supply explicit illustrations of\nthese computed solutions.\u003c\/p\u003e \u003ch3\u003eDetails\u003c\/h3\u003e \u003cp\u003ePublished by: Springer\u003c\/p\u003e \u003cp\u003ePublication Date: 2018-06-14\u003c\/p\u003e \u003cp\u003eFormat: Paperback\u003c\/p\u003e \u003cp\u003eISBN-13: 9783319801629\u003c\/p\u003e \u003cp\u003eDOI: 10.1007\/978-3-319-27526-0\u003c\/p\u003e \u003cp\u003eDimensions: 235cm x155cm\u003c\/p\u003e \u003cp\u003ePages: 226\u003c\/p\u003e ","brand":"Springer International Publishing","offers":[{"title":"Default Title","offer_id":46547984515212,"sku":"9783319801629","price":98.99,"currency_code":"USD","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0710\/9545\/1788\/files\/9783319801629.jpg?v=1776021750","url":"https:\/\/fh90cf-fv.myshopify.com\/products\/9783319801629","provider":"Late Knight Books and Services, LLC","version":"1.0","type":"link"}