On a global unique solvability of some two-dimensional problems for the water solutions of polymers

A global unique solvability of the two-dimensional unitial boundary value problem with some slip-boundary conditions for a quasilinear system describing the flows of weak water solutions of polymers is proved. It is noted that for this system a global unique solvability of the Cauchy problem and the initial boundary problem with the periodic boundary conditions are proved in a similar way.