On well-posedness of Navier–Stokes variational inequalities

Abstract

In this paper, well-posedness is carried out on variational inequalities in a general form for the stationary Navier–Stokes equations modeling viscous incompressible fluid flows with a nonsmooth slip boundary condition of friction type. For a special form of the variational inequality commonly studied in existing literature, our proof technique leads to a substantial improvement on the well-posedness condition.