Analysis of Stokes system with solution-dependent subdifferential boundary conditions

Abstract We study the Stokes problem for incompressible fluid with mixed nonlinear boundary conditions of subdifferential type. The latter involve a unilateral condition, Navier slip nonmonotone version Navier–Fujita and threshold leak condition frictional weak form leads to new class variational–hemivariational inequalities on convex sets velocity field. Solution existence compactness solution set inequality are established based Schauder fixed point theorem.