Three approaches for the rigorous study of the 2D Navier-Stokes equations (
NSE) are applied to the Lorenz system. Analysis of time averaged solutions
leads to a description of invariant probability measures on the Lorenz attr
actor which is much more complete than what is known for the NSE. As is the
case for the NSE, solutions on the Lorenz attractor are analytic in a stri
p about the real time axis. Rigorous estimates are combined with numerical
computation of Taylor coefficients to estimate the width of this strip. App
roximate inertial forms originally developed for the NSE are analyzed for t
he Lorenz system, and the dynamics for the latter are completely described.