Steady-State Solutions to the Equations of Motion of Second-Grade Fluids with General Navier Type Slip Boundary Conditions in Holder Spaces

Abstract

We consider a boundary-value problem for the stationary flow of an incompressible second-grade fluid in a bounded domain. The boundary condition allows for no-slip, Navier type slip, and free slip on different parts of the boundary. We first establish the well-posedness of a linear auxiliary problem by means of a fixed-point argument in which the problem is decomposed into a Stokes-type problem and two transport equations. Then we use the method of successive approximations to prove the unique solvability of the nonlinear problem with a sufficiently small body force in Holder spaces. Bibliography: 17 titles.