Abstract
We study a new class of abstract evolution variational–hemivariational inequalities with constraints in the framework of evolution triples of spaces. Existence of solution is established based on the so-called mixed equilibrium problem formulation. Then, we apply this result to a mathematical analysis of the unsteady Oseen model for a generalized Newtonian incompressible fluid. A variational–hemivariational inequality for the flow problem is derived and sufficient conditions for existence of weak solutions are obtained. The mixed boundary conditions involve a unilateral boundary condition, the Navier slip condition, a nonmonotone version of the nonlinear Navier–Fujita slip condition, and the threshold slip and leak condition of frictional type.
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