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

Authors: Stenger, Frank, Tucker, Don, Baumann, Gerd

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  • Studies the properties of solutions of the Navier–Stokes partial differential equations on (x , y, z , t) ∈ ℝ3 × [0, T]
  • Demonstrates a new method for determining solutions of the Navier–Stokes equations by converting partial differential equations to a system of integral equations describing spaces of analytic functions containing solutions
  • Enables sharper bounds on solutions to Navier–Stokes equations, easier existence proofs, and a more accurate, efficient method of determining a solution with accurate error bounds
  • Includes an custom-written Mathematica package for computing solutions to the Navier–Stokes equations based on the author's approximation method
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eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-319-27526-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-27524-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-3-319-80162-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
About this 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.

Table of contents (6 chapters)

Table of contents (6 chapters)

Buy this book

eBook $84.99
price for USA in USD (gross)
  • ISBN 978-3-319-27526-0
  • Digitally watermarked, DRM-free
  • Included format: EPUB, PDF
  • ebooks can be used on all reading devices
  • Immediate eBook download after purchase
Hardcover $109.99
price for USA in USD
  • ISBN 978-3-319-27524-6
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
Softcover $109.00
price for USA in USD
  • ISBN 978-3-319-80162-9
  • Free shipping for individuals worldwide
  • Usually dispatched within 3 to 5 business days.
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Bibliographic Information

Bibliographic Information
Book Title
Navier–Stokes Equations on R3 × [0, T]
Authors
Copyright
2016
Publisher
Springer International Publishing
Copyright Holder
Springer International Publishing AG
eBook ISBN
978-3-319-27526-0
DOI
10.1007/978-3-319-27526-0
Hardcover ISBN
978-3-319-27524-6
Softcover ISBN
978-3-319-80162-9
Edition Number
1
Number of Pages
X, 226
Number of Illustrations
25 illustrations in colour
Topics