Journal of Statistical Physics, Vol. 44, Nos. 1/2, 1986, p. 107-128
In two and three dimensions, the relaxation time Bottzmann equation can be
solved analytically for the distribution function for a system of two hard par-
ticles subject to isothermal shear. The previous solutions of Morriss, and Ladd
and Hoover are shown to be formally equivalent. The integral representation for
the average of each of the elements of the pressure tensor in the steady state is
obtained for both sllod and dolls tensor equations of motion. Rigorous
equations are derived which relate the viscosity and the normal stress differences
in these two methods. We obtain asymptotic expansions for each element of the
pressure tensor for both small and large 7. For high shear rates, the viscosity is
found to vanish as 7 -2 log y in both two and three dimensions.