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 this paper, we prove the existence of weak solutions to the initial-boundary value problem that describes the motion of weakly concentrated aqueous solutions of polymers. The proof is based on the approximation-topological approach. At the first step, we approximate the operator equation, which is equivalent to the weak statement of the considered problem, with another operator equation with “good” properties and prove the solvability of the latter equation. At the second step, we proceed to the limit, i.e., we prove that the sequence of solutions contains a subsequence that converges weakly to the solution of the initial problem as the approximation parameter tends to zero.