An alpha-model of polymer solutions motion

The initial–boundary value problem for the alpha–model describing the motion of weakly concentrated aqueous polymer solutions is investigated at the paper. The considered mathematical model is studied with the rheological relation satisfing the objectivity principle. The weak solutions existence for the alpha–model is proved on the based of the topological approximation apporoach for hydrodynamic problems study. Also the convergence of alpha–models solutions to a solution of the original model is proved when alpha tends to zero.