SINGULAR BEHAVIOR OF THE VELOCITY MOMENTS OF A DILUTE GAS UNDER UNIFORM SHEAR-FLOW

The hierarchy of moment equations derived from the nonlinear Boltzmann equation describing uniform shear flow is analyzed. It is shown that all the moments of order k greater than or equal to 4 diverge in time for shear rates larger tha na critical value a(c)((k)), which decrease s as k increases. Furthermore, the results suggest an asymptotic behav ior of the form a(c)((k)) similar to k(-mu) for large k. Consequently, even for very small shear rates, either a stationary solution fails t o exist (which implies the absence of a normal solution) or a stationa ry solution exists but with only a finite number of convergent moments . Although the uniform shear how may be experimentally unrealizable fo r large shear rates, the above conclusions can be of interest for more realistic flows.