= Dust gravitational dispersion relation with gas drag
{title2=$s[(s+\epsilon\Omega)^2+\Omega^2]+(c^2k^2-2\pi G\sigma_0|k|)(s+\epsilon\Omega)=0$}
The local axisymmetric density/velocity system of a pressured dust layer with linear <gas drag> and a fixed <Keplerian shearing sheet> gas flow has this cubic <dispersion relation>. The $\Omega/2$ azimuthal velocity coefficient includes advection of the <Keplerian shear>. The <razor-thin disk Poisson kernel> supplies the $|k|$ self-gravity term. Keeping the full amplitude <determinant> retains the zero-frequency branch and avoids dividing out the secular mode.
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