A generalized Stokes system with a nonsmooth slip boundary condition

TL;DR

This paper studies a complex class of inequalities in Banach spaces, establishing well-posedness and applying the results to a fluid dynamics model with a nonmonotone slip boundary condition.

Contribution

It introduces a generalized Stokes system with a nonsmooth slip boundary condition and proves existence, uniqueness, and stability of solutions.

Findings

Well-posedness of the inequality system established.

Existence and uniqueness of solutions proven.

Application to a fluid model with slip boundary condition demonstrated.

Abstract

A class of quasi-variational-hemivariational inequalities in reflexive Banach spaces is studied. The inequalities contain a convex potential, a locally Lipschitz superpotential, and an implicit obstacle set of constraints. Results on the well posedness are established including existence, uniqueness, dependence of solution on the data, and the compactness of the solution set in the strong topology. The applicability of the results is illustrated by the steady-state Stokes model of a generalized Newtonian incompressible fluid with a nonmonotone slip boundary condition.