= Solution
The <Jeans equations> express local momentum conservation for a <collisionless stellar system>, just as the <Euler equations> do for a gas. The mean streaming <velocity> plays the role of fluid flow, the gravitational force is a body force, and random stellar motions supply a <pressure tensor> through $\rho\sigma_{ij}^2$. Taking moments smooths over individual stellar orbits and produces fields of <density>, mean <velocity> and random-motion stress; this is the sense of “stellar hydrodynamics”.
Ordinary gas <pressure> is usually nearly isotropic because collisions relax its local <velocity> distribution. A <collisionless stellar system> can retain an anisotropic <velocity ellipsoid>, so its <pressure tensor> is not generally a scalar times the identity. There are more unknown second moments than momentum equations, and their evolution introduces higher moments. The <Jeans equations> therefore require further dynamical assumptions or a specified <one-particle distribution function> for closure; they do not by themselves establish local <thermal equilibrium> or a gas <equation of state>.
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