Mixed boundary-value problems for motion equations of a viscoelastic medium

We study the mixed boundary-value problem for steady motion equations of an incompressible viscoelastic medium of Jeffreys type in a fixed three-dimensional domain. On one part of the boundary the no-slip condition is provided, while on the other one the impermeability condition and non-homogeneous Dirichlet boundary conditions for tangential component of the surface force is used. The existence of weak solutions of the formulated boundary-value problem is proved. Some estimates for weak solutions are established; it is shown that the set of weak solutions is sequentially weakly closed