Abstract
The high-velocity distribution of a two-dimensional dilute gas of Maxwell molecules under uniform shear flow is studied. First we analyze the shear-rate dependence of the eigenvalues governing the time evolution of the velocity moments derived from the Boltzmann equation. As in the three-dimensional case discussed by us previously, all the moments of degreek⩾4 diverge for shear rates larger than a critical valuea (k)c , which behaves for largek asa (k)c ∼k −1. This divergence is consistent with an algebraic tail of the formf(V) ∼V −4-σ(a), where σ is a decreasing function of the shear rate. This expectation is confirmed by a Monte Carlo simulation of the Boltzmann equation far from equilibrium.
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Montanero, J.M., Santos, A. & Garzó, V. Distribution function for large velocities of a two-dimensional gas under shear flow. J Stat Phys 88, 1165–1181 (1997). https://doi.org/10.1007/BF02732430
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DOI: https://doi.org/10.1007/BF02732430