On weak solutions to evolution equations of viscoelastic fluid flows

We study the system of nonlinear equations describing unsteady flows of a viscoelastic fluid of Oldroyd type in a bounded three-dimensional domain with mixed boundary conditions. On one part of the boundary, the Navier slip condition is given, while on the other one, the no-slip condition is used. We prove the theorem on the existence, uniqueness, and energy estimates for weak solutions.