  The 3D spatially periodic Navier-Stokes equation is posed as a nonlinear
matrix differential equation. When the flow is assumed to be a time series
having unknown wavenumber coefficients, then the matrix in this periodic
Navier-Stokes matrix differential equation becomes a time series of matrices.
Posed in this way, any flow's unknown wavenumber coefficients can be solved for
recursively beginning with the zeroth-order coefficient representing any
initial flow. When all matrices in the time series commute, a flow's unknown
coefficients also represent the Taylor expansion of a stable matrix exponential
product operating on the initial flow. This paper argues that a solution's
coefficients converge to these bounded Taylor coefficients when these bounds
are evaluated with a general solution's noncommutative matrices.
