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1 Kinetic Equations: From Newton to Boltzmann
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The classical example for a collisional model of the form (1.8) is encountered
in the kinetic theory of rarified gases.
Actually, most of the gas flows around us are rather accurately modeled by
macroscopic flow equations (the viscous Navier–Stokes or the inviscid Euler
system, see Chapter 2). However, it is nevertheless of paramount importance
to understand the underlying flow dynamics from a microscopic ‘molecular’
point of view. A main reason for this is that we need to know the physical
limits of validity of macroscopic flow equations, which are based on microscopic
dynamics.
Typical gaseous flow examples can be seen in the Images 1.1–1.6, showing an
airplane in its take-off phase (Image 1.1) and various (meteorological) clouds
(Images 1.2–1.6), among them images with a front of clouds being convected by
a strong wind towards a high mountain(Images 1.3, 1.4). Note that fluid dynamic
modeling of airplane flow and cloud dynamics may still give sufficiently accurate
results for many practical purposes (see the comments to the images below). For
somemoreexoticcasesofrarifiedgasflowmacroscopicequationsarecompletely
insufficient and a microscopic model has to be employed directly.

Fig. 1.2. Altocumulus lenticularis duplicatus over the planes of Patagonia