On weak solutions to evolution equations of viscoelastic fluid flows

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