Investigation of a problem governing a steady flow of the second grade fluid in the Hölder classes of functions

The paper concerns the boundary-value problem (with a usual adherence boundary condition) for a stationary system of equations of motion of the second grade fluids in a bounded domain. This system is not elliptic and it contains third order derivatives of the velocity vector field that introduces obvious difficulties into the analysis of the above problem. It is known that it reduces to the usual Stones problem and to the transport equations or its analogues. We present a new, somewhat easier method of such a reduction which made it possible to prove the solvability of a stationary boundary value problem for the equations of motion of the second grade fluids in the Hölder classes of functions in the case of small exterior forces.