# Hilbert's 6th problem: Exact and approximate hydrodynamic manifolds for kinetic equations

@article{Gorban2013Hilberts6P, title={Hilbert's 6th problem: Exact and approximate hydrodynamic manifolds for kinetic equations}, author={Alexander N. Gorban and Iliya V. Karlin}, journal={Bulletin of the American Mathematical Society}, year={2013}, volume={51}, pages={187-246} }

The problem of the derivation of hydrodynamics from the Boltz- mann equation and related dissipative systems is formulated as the problem of slow invariant manifold in the space of distributions. We review a few in- stances where such hydrodynamic manifolds were found analytically both as the result of summation of the Chapman-Enskog asymptotic expansion and by the direct solution of the invariance equation. These model cases, comprising Grad's moment systems, both linear and nonlinear, are…

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