On exact analytical solutions of equations of Maxwell incompressible viscoelastic medium

Unsteady two-dimensional flows of incompressible viscoelastic Maxwell medium with upper, low and corotational convective derivatives in the rheological constitutive law are considered. A class of partially invariant solutions is analyzed. Using transition to Lagrangian coordinates, an exact solution of the problem of unsteady flow near free-stagnation point was constructed. For the model with Johnson–Segalman convected derivative and special linear dependence of the vertical component of velocity, the general solutions were derived. •A class of partially invariant solutions is analyzed.•Exact solution in Lagrangian coordinates was found.•General solutions for α=−1,0,1 of the Johnson-Segalman model were derived.