  The uniform shear flow for the rarefied gas is governed by the time-dependent
spatially homogeneous Boltzmann equation with a linear shear force. The main
feature of such flow is that the temperature may increase in time due to the
shearing motion that induces viscous heat and the system becomes far from
equilibrium. For Maxwell molecules, we establish the unique existence,
regularity, shear-rate-dependent structure and non-negativity of self-similar
profiles for any small shear rate. The non-negativity is justified through the
large time asymptotic stability even in spatially inhomogeneous perturbation
framework, and the exponential rates of convergence are also obtained with the
size proportional to the second order shear rate. The analysis supports the
numerical result that the self-similar profile admits an algebraic
high-velocity tail that is the key difficulty to overcome in the proof.
