DISTRIBUTION FUNCTION FOR LARGE VELOCITIES OF A 2-DIMENSIONAL GAS UNDER SHEAR-FLOW

The high-velocity distribution of a two-dimensional dilute gas of Maxw ell molecules under uniform shear flow is studied. First we analyze th e shear-rate dependence of the eigenvalues governing the time evolutio n of the velocity moments derived from the Boltzmann equation. As in t he three-dimensional case discussed by us previously, all the moments of degree k greater than or equal to 4 diverge for shear rates larger than a critical value a(c)((k)), which behaves for large k as a(c)((k) ) similar to k(-1). This divergence is consistent with an algebraic ta il of the form f(V) similar to V-4-sigma(a), where sigma is a decreasi ng function of the shear rate. This expectation is confirmed by a Mont e Carlo simulation of the Boltzmann equation far from equilibrium.