The Navier-Stokes-Voigt equations with position-dependent slip boundary conditions

We consider an initial-boundary value problem for the Navier-Stokes-Voigt equations with a general position-dependent Navier-type slip boundary condition, which is formulated in terms of the curl operator. This system models unsteady flows of an incompressible viscoelastic fluid in a 3D bounded domain with impermeable heterogeneous boundary. The existence of a unique weak solution, global in time, is proved for arbitrary large data from suitable function spaces. We also study the long-time asymptotic behavior of the velocity field under the assumption that the external forces field is conservative.