Abstract
In this chapter, we will review some analytical methods that make it possible to determine approximate solutions of the Boltzmann equation. In particular, we will discuss the structure of the Hilbert and Chapman–Enskog perturbation techniques and will also outline the essential features of the invariant manifold method, which stems from the assumption of time scale separation and, unlike the former methods, is also applicable beyond the strict hydrodynamic limit. Before reviewing the wealth of different techniques, it is worth investigating in greater depth the role of the different time scales in a particle system, which is one of the main ingredients underlying the onset of collective behavior.
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© 2013 Matteo Colangeli
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Colangeli, M. (2013). Methods of Reduced Description. In: From Kinetic Models to Hydrodynamics. SpringerBriefs in Mathematics. Springer, New York, NY. https://doi.org/10.1007/978-1-4614-6306-1_3
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DOI: https://doi.org/10.1007/978-1-4614-6306-1_3
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