= Pressureless dust fluid in a shearing sheet
A dilute dust component can be approximated as a pressureless fluid with velocity $\mathbf v$ and <surface density of a disk> $\Sigma_d$. In a gas velocity $\mathbf u$, linear <drag force> gives acceleration $-(\mathbf v-\mathbf u)/t_s$ for positive <aerodynamic stopping time> $t_s$. Its equations include <Coriolis acceleration>, the <shearing-sheet tidal potential>, and $\partial_t\Sigma_d+\nabla\cdot(\Sigma_d\mathbf v)=0$. Neglecting gas backreaction is justified only when the prescribed-gas approximation is appropriate. Strong orbit crossing or appreciable dust velocity dispersion can invalidate the single-valued pressureless-fluid description.
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