  We study the long time asymptotics of a modified compressible Navier-Stokes
system (mcNS) inspired by the previous work of Hoff and Zumbrun. We introduce a
new decomposition of the momentum field into its irrotational and
incompressible parts, and a new method for approximating solutions of the heat
equation in terms of Hermite functions in which $n^{th}$ order approximations
can be computed for solutions with $n^{th}$ order moments. We then obtain
existence of solutions to the mcNS system and show that the approximation in
terms of Hermite functions gives the leading order terms in the long-time
asymptotics, and under certain assumptions can be evaluated explicitly.
