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On the derivation of hydrodynamics from the Boltzmann equation. (English) Zbl 1147.76383

The authors review the main ideas on the derivation of hydrodynamical equations from microscopic models. The Boltzmann equation, which is a good approximation for the evolution of rare gases, provides a useful tool to test these ideas in mathematically controllable situations such as the Euler and incompressible Navier-Stokes limits, which we describe in some detail. We also discuss the heuristics and some rigorous results available for stochastic particle systems.
Reviewer: R. Esposito

MSC:

82C40 Kinetic theory of gases in time-dependent statistical mechanics
76A02 Foundations of fluid mechanics
76P05 Rarefied gas flows, Boltzmann equation in fluid mechanics
76D05 Navier-Stokes equations for incompressible viscous fluids
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