On the Weak Solvability of a Mathematical Model Describingthe Motion of Polymer Solutionswith Memory

The paper considers the weak solvability of the initial–boundary value problem describing the motion of weakly concentrated aqueous polymer solutions taking into account the memory of the fluid. In this model, the memory is considered along the trajectory of fluid particles determined by the velocity field. The topological approximation approach and the theory of regular Lagrangian flows are used.