A new class of variational‐hemivariational inequalities for steady Oseen flow with unilateral and frictional type boundary conditions

Abstract

AbstractWe study a new class of elliptic variational‐hemivariational inequalities in a reflexive Banach space. Based on a surjectivity result for an operator inclusion of Clarke's subdifferential type, we prove existence of solution. Then, we apply this result to a mathematical analysis of the steady 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.