  The density wave theory for the grand-design two-armed spiral pattern in
galaxies is successful in explaining several observed features. However, the
long-term persistence of this spiral structure is a serious problem since the
group transport would destroy it within about a billion years as shown in a
classic paper by Toomre. In this paper we include the low velocity dispersion
component, namely gas, on an equal footing with stars in the formulation of the
density wave theory, and obtain the dispersion relation for this coupled
system. We show that the inclusion of gas makes the group transport slower by a
factor of few, thus allowing the pattern to persist longer - for several
billion years. Though still less than the Hubble time, this helps in making the
spiral structure more long-lived. Further we show that addition of gas is
essential to get a stable wave for the observed pattern speed for the Galaxy,
which otherwise is not possible for a one-component stellar disc.
