William McLeod Rivera
A Fourier Series approach to solving the Navier-Stokes Equations with Spatially Periodic Data 
(523K, pdf)

ABSTRACT.  The symbol U=(u,v,w) denotes the velocity or momentum (the mass multiplied by the velocity). I transform the Navier Stokes momentum and density equations into infinite systems of ordinary differential and linear equations for the classical Fourier coefficients. I prove theorems on existence, uniqueness and smoothness of solutions. I interpret the results using the Fourier series representation of (U,P) .