Studies the properties of solutionsof the Navier-Stokes partial differential equations on (x, y, z, t) ? R3 × [0, T]Demonstrates a new method fordetermining solutions of the Navier-Stokes equations by converting partialdifferential equations to a system of integral equations describing spaces ofanalytic functions containing solutionsEnables sharper bounds on solutions to NavierStokes equations, easier existence proofs, and a more accurate, efficient method of determining a solution with accurate error boundsIncludes an custom-written Mathematica package for computing solutions to the Navier-Stokes equations based on the author's approximation methodIncludes supplementary material: sn.pub/extras