The Linearized Collision Operator
In Chapter II we found a solution of the Boltzmann equation, i.e., the Maxwellian. It is an exact solution of the Boltzmann equation and the most significant and widely used solution [other interesting solutions have been found but there is not sufficient space to discuss them here; some of them are discussed in detail in a book by Truesdell and Muncaster (ref. 1); see also Chapter VII, Section 14]. The meaning of the Maxwellian distribution is clear: it describes equilibrium states (or slight generalizations of them), characterized by the fact that neither heat flow nor stresses other than isotropic pressure are present. If we want to describe more realistic non-equilibrium situations, when oblique stresses are present and heat transfers take place, we have to rely upon approximation methods.
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