Mathematical models of polymer solutions motion and their symmetries

Exact Solutions of Boundary Layer Equations in Polymer Solutions

“…The first solution ( 6) and (7), which satisfies the no-slip condition at y = 0 and is bounded as y → ∞, is derived by the method of differential constraints. The representations of the other two solutions (13) and (16) were obtained by noting that 1, exp(y/s(t)) and cos(y/s(t)) are elements of invariant subspaces of Equation (11). It should also be noted that Equation (11) was obtained as the reduced equation for a partially invariant solution [14] of the admitted Lie algebra (9).…”

“…The representations of the other two solutions (13) and (16) were obtained by noting that 1, exp(y/s(t)) and cos(y/s(t)) are elements of invariant subspaces of Equation (11). It should also be noted that Equation (11) was obtained as the reduced equation for a partially invariant solution [14] of the admitted Lie algebra (9). The main feature of these solutions is that they are reduced to solving ordinary differential equations.…”

“…Stationary solutions of system (1) were analyzed in [8,9]. The group properties of Equation (1) and the construction of their exact solutions were studied in [2,[10][11][12].…”

Analysis of the Models of Motion of Aqueous Solutions of Polymers on the Basis of Their Exact Solutions

“…The absence of the boundary layer near the solid boundary as κ → 0 was previously detected in the problem of polymer solution motion near the stagnation point [36,39,40].…”

“…Such an example for Navier-Stokes equations is the solution of an unsteady problem of motion near the stagnation point [38]. The problem of a stagnation point flow of an aqueous solution of a polymer was studied in Reference [39] (plane steady problem), Reference [36] (plane unsteady problem), and Reference [40] (axisymmetric steady flow).…”