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

In this monograph, leading researchers inthe world of numerical analysis, partial differential equations, and hardcomputational problems study the properties of solutions of the Navier-Stokes partialdifferential equations on (x, y, z, t) ? ?3 × [0, T]. Initially converting the PDE to asystem of integral equations, the authors then describe spaces A of analytic functions that housesolutions of this equation, and show that these spaces of analytic functionsare dense in the spaces S of rapidlydecreasing and infinitely differentiable functions. This method benefits fromthe 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 boundsFollowing the proofs of denseness, theauthors prove the existence of a solution of the integral equations in thespace of functions A ? ?3 × [0, T], and provide an explicit novel algorithm based on Sincapproximation and Picard-like iteration for computing the solution.Additionally, the authors include appendices that provide a custom Mathematicaprogram for computing solutions based on the explicit algorithmic approximationprocedure, and which supply explicit illustrations of these computed solutions.