= Razor-thin fluid disk dispersion relation
{title2=$(\omega-n\Omega)^2=\kappa^2+a_0^2k^2-2\pi G\Sigma|k|$}
For tightly wound perturbations in a locally uniform, razor-thin <gas> disk, <continuity equation> and rotating-fluid <momentum> equations couple the surface-density perturbation to radial and azimuthal velocities. The sheet potential is $\delta\Phi=-2\pi G\delta\Sigma/|k|$. Eliminating these perturbations gives the displayed <dispersion relation>. <radial epicyclic frequency> supplies the <rotation> term, the sound-speed term resists short waves, and <self-gravity> supplies the negative term. For an axisymmetric mode $n=0$, use $\omega^2$ directly; the <pattern speed> $\omega/n$ is undefined.
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