Abstract
The known solution to the spatially homogeneous nonlinear Boltzmann equation for Maxwell models in a series of Laguerre polynomials is extended to include nonisotropic initial conditions. Existence proofs for a class of solutions are supplied. The equations for the generalized (nonisotropic Laguerre) moments are derived in explicit form for two- and three-dimensional models. Further it is shown that the ordinary moments satisfy the same set of equations as the (Hermite) polynomial moments.
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Hendriks, E.M., Nieuwenhuizen, T.M. Solution to the nonlinear boltzmann equation for maxwell models for nonisotropic initial conditions. J Stat Phys 29, 591–615 (1982). https://doi.org/10.1007/BF01342189
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DOI: https://doi.org/10.1007/BF01342189