{"product_id":"navier-stokes-equations-on-r3-x-0-t-9783319801629","title":"Navier-Stokes Equations on R3 × [0, T]","description":"\u003cp\u003e • Author(s): Frank Stenger\u003cbr\u003e • Publisher: Springer\u003cbr\u003e • Publisher Imprint: Springer\u003cbr\u003e • BISAC: Differential Equations - General\u003c\/p\u003e\u003cp\u003e\u003c\/p\u003e\u003cp\u003e\u003cb\u003eFrom the Back Cover\u003c\/b\u003e\u003cbr\u003e\u003c\/p\u003e\u003cp\u003eIn this monograph, leading researchers in the world of numerical analysis, partial differential equations, and hard computational problems study the properties of solutions of the Navier-Stokes\u003cb\u003e \u003c\/b\u003epartial differential equations on (x, y, z, t) ∈ ℝ\u003csup\u003e3\u003c\/sup\u003e × [0, \u003ci\u003eT\u003c\/i\u003e]. Initially converting the PDE to a system of integral equations, the authors then describe spaces \u003cb\u003eA\u003c\/b\u003e of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces \u003ci\u003eS\u003c\/i\u003e of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages: \u003c\/p\u003e\u003cul\u003e \u003cli\u003eThe functions of S are nearly always conceptual rather than explicit\u003c\/li\u003e \u003cli\u003eInitial and boundary conditions of solutions of PDE are usually drawn from the applied sciences, and as such, they are nearly always piece-wise analytic, and in this case, the solutions have the same properties\u003c\/li\u003e \u003cli\u003eWhen methods of approximation are applied to functions of \u003cb\u003eA\u003c\/b\u003e they converge at an exponential rate, whereas methods of approximation applied to the functions of \u003cb\u003eS\u003c\/b\u003e converge only at a polynomial rate\u003c\/li\u003e \u003cli\u003eEnables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds\u003c\/li\u003e \u003c\/ul\u003e\u003cp\u003e \u003c\/p\u003e\u003cp\u003eFollowing the proofs of denseness, the authors prove the existence 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 algorithm based on Sinc approximation and Picard-like iteration for computing the solution. Additionally, the authors include appendices that provide a custom Mathematica program for computing solutions based on the explicit algorithmic approximation procedure, and which supply explicit illustrations of these computed solutions.\u003c\/p\u003e","brand":"Springer","offers":[{"title":"Paperback","offer_id":45274607386775,"sku":"9783319801629","price":7345.0,"currency_code":"INR","in_stock":true}],"thumbnail_url":"\/\/cdn.shopify.com\/s\/files\/1\/0666\/3471\/1191\/files\/9783319801629.webp?v=1769280491","url":"https:\/\/atlanticbooks.com\/products\/navier-stokes-equations-on-r3-x-0-t-9783319801629","provider":"Atlantic Books","version":"1.0","type":"link"}