In this monograph, leading researchers in the world ofnumerical analysis, partial differential equations, and hard computationalproblems study the properties of solutions of the Navier-Stokes partial differential 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:
Following the proofs of denseness, the authors prove theexistence of a solution of the integral equations in the space of functions A 3 × [0, T], and provide an explicit novelalgorithm based on Sinc approximation and Picard-like iteration for computingthe solution. Additionally, the authors include appendices that provide acustom Mathematica program for computing solutions based on the explicitalgorithmic approximation procedure, and which supply explicit illustrations ofthese computed solutions.