= Hydrodynamic limit of the Boltzmann equation
In a scaling $\partial_tf+v\cdot\nabla_xf=\varepsilon^{-1}Q(f,f)$ with small <Knudsen number>, the leading collision balance formally forces a <local Maxwellian>. The conserved moments then give the <Euler equations> with a monatomic ideal-gas closure. The next nonequilibrium correction produces viscous and heat-conduction terms. These substitutions are formal: rigorous limits need uniform estimates, initial and boundary conditions, and sufficient convergence.
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