The existence theorem for a weak solution to initial-boundary value problem for system of equations describing the motion of weak aqueous polymer solutions

In the paper we prove the existence of weak solutions for the initial-boundary value problem describing the motion of weakly concentrated aqueous solutions of polymers. The proof is based on the approximation-topological approach. At the first step we prove the operator equation which is equivalent to the weak formulation of the considered problem is approximated by another operator equation with good properties and the solvability of this equation. At the second step, the passage to the limit is made, i. e., it is shown that from a sequence of solutions one can extract a subsequence that converges weakly to the solution of the original problem as the parameter of approximation tends to zero.