On well-posedness of a hydrodynamic model of interaction of a medium with a rigid wall (Q1357963)

The article studies a model of interaction of a viscous medium with a wall. The physical meaning of the model is as follows: if a force acts on a fluid, separating it from the wall, then a free surface must be formed. A series of boundary problems, where the classical ``adhesion'' condition is replaced with some inequalities, is considered. In particular, some results for gases with rather general equation of state are obtained. The author proves existence theorems under some natural constraints, and examines the uniqueness of the solution. It turns out that the uniqueness fails, in general.