  We derive general conditions of slip of a fluid on the boundary. Under these
conditions the velocity of the fluid on the immovable boundary is a function of
the normal and tangential components of the force acting on the surface of the
fluid. A problem on stationary flow of an electrorheological fluid in which the
terms of slip are specified on one part of the boundary and surface forces are
given on the other is formulated and studied. Existence of a solution of this
problem is proved by using the methods of penalty functions, monotonicity and
compactness. It is shown that the method of penalty functions and the Galerkin
approximations can be used for the approximate solution of the problem under
consideration.
