Problem on stationary flow of electrorheological fluids at the generalized conditions of slip on the boundary

Abstract

General conditions of slip of a fluid on the boundary are derived anda problem on stationary flow of the electrorheological fluid in which the terms of slip are specifiedon one part of the boundary and surface forces are given on the otheris formulated and studied. Existence of a generalized (weak) solution of this problem is provedby using the methods of penalty functions, monotonicity and compactness.It is shown that the method of penalty functions and the Galerkinapproximations can be used for the approximatesolution of the problem under consideration. The existence and the uniqueness of the smooth classical solution of the problem is proved in the case that the conditions of slip are prescribed on the whole of the boundary.