Stationary variational inequalities in a model of an inhomogeneous incompressible fluid (Q1972650)

A steady flow of non-homogeneous viscous incompressible fluid in a bounded simply connected region is considered. Nonlinear boundary conditions are described with the help of subdifferential relations. Under this approach, the classical boundary conditions are a special case of subdifferential conditions. The main result of the article is an existence theorem for a generalized solution to a boundary value problem. The theorem obtained is applied to some particular problems, namely, to the problem with fixed total pressure along the boundary, one-sided boundary value problem, and Dirichlet problem.