In a polydomain model for textured liquid-crystalline polymers, domain shrinkage and texture coarsening at low shear rates are considered to be driven by the deviations of defect density L from the initial (L0) and steady (L(s)) states, respectively. The densities of L0 and L(s) correspond to the average domain sizes of a0 and a(s) at each state. The introduction of L0 into the Larson-Doi defect density evolution equation provides a limit of texture length scale, eliminating the indefinite coarsening of texture. Then, the defect density evolution is refreshed in each case of the steady state, shear inception, and shear cessation. With the inclusion of L0, the shear thinning behavior of a steady-state viscosity curve can be developed in Onogi-Asada’s region I as well as the Newtonian plateau behavior in region II. Moreover, another Newtonian plateau region over very low shear rates, called "region 0," can be predicted when smaller domains are considered to be isotropically distributed at the initial state.