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Navier-Stokes Equations on R3 × [0, T]

Navier-Stokes Equations on R3 × [0, T]

          
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About the Book

In 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 partial differential equations on (x, y, z, t) ∈ ℝ3 × [0, T]. Initially converting the PDE to a system of integral equations, the authors then describe spaces A of analytic functions that house solutions of this equation, and show that these spaces of analytic functions are dense in the spaces S of rapidly decreasing and infinitely differentiable functions. This method benefits from the following advantages:

  • The functions of S are nearly always conceptual rather than explicit
  • Initial 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
  • When methods of approximation are applied to functions of A they converge at an exponential rate, whereas methods of approximation applied to the functions of S converge only at a polynomial rate
  • Enables sharper bounds on the solution enabling easier existence proofs, and a more accurate and more efficient method of solution, including accurate error bounds

Following the proofs of denseness, the authors prove the existence of a solution of the integral equations in the space of functions A ∩ ℝ3 × [0, T], 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.


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Product Details
  • ISBN-13: 9783319275246
  • Publisher: Springer
  • Publisher Imprint: Springer
  • Edition: 1st ed. 2016
  • Language: English
  • Returnable: Y
  • Spine Width: 14 mm
  • Width: 156 mm
  • ISBN-10: 3319275240
  • Publisher Date: 04 Oct 2016
  • Binding: Hardback
  • Height: 234 mm
  • No of Pages: 226
  • Series Title: English
  • Weight: 512 gr


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