On weak solutions for some model of motion of nonlinear viscoelastic fluid (Q1580018)

The authors consider an initial-boundary value problem for a nonlinear incompressible viscoelastic fluid. The corresponding constitutive equation generalizes the Oldroyd model describing both laminar and turbulent flows. It is assumed that the non-slip condition holds on a part of the boundary, and another part of the boundary undergoes the action of a force acting on the fluid surface. The problem is rewritten in an equivalent operator form, and the properties of the corresponding operator are investigated. The existence theorem is proved by using approximating operator equations.