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Solutions of the moment hierarchy in the kinetic theory of Maxwell models

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Abstract

In the Maxwell interaction model the collision rate is independent of the relative velocity of the colliding pair and, as a consequence, the collisional moments are bilinear combinations of velocity moments of the same or lower order. In general, however, the drift term of the Boltzmann equation couples moments of a given order to moments of a higher order, thus preventing the solvability of the moment hierarchy, unless approximate closures are introduced. On the other hand, there exist a number of states where the moment hierarchy can be recursively solved, the solution generally exposing non-Newtonian properties. The aim of this paper is to present an overview of results pertaining to some of those states, namely the planar Fourier flow (without and with a constant gravity field), the planar Couette flow, the force-driven Poiseuille flow, and the uniform shear flow.

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    Andrés Santos

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Santos, A. Solutions of the moment hierarchy in the kinetic theory of Maxwell models. Continuum Mech. Thermodyn. 21, 361–387 (2009). https://doi.org/10.1007/s00161-009-0113-5

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