= Weak-drag dust density waves
{title2=$s_\pm=\pm i\omega-\epsilon\Omega(\omega^2+\Omega^2)/(2\omega^2)+O(\epsilon^2)$}
For fixed $\omega^2=\Omega^2-2\pi G\sigma_0|k|+c^2k^2>0$, the two oscillatory roots of the <dust gravitational dispersion relation with gas drag> acquire negative real parts at first order in $\epsilon$. Their frequencies have no first-order shift. The expansion is not uniform near $\omega^2=0$, where the oscillation and damping scales can become comparable.
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