Stokes Flows Imposed Constant Navier Slip Length on Boundary for Domains of Simple Geometry (Advances in Applied Mathematics and Mechanics, 2025)
In micro-nano and even some macro-scale flows, the boundary slip cannotbe ignored and has an important influence. We consider the most widely used Navierslip length model to investigate whether the solution of Stokes flow exists if a homogeneous slip is imposed as a boundary condition replacing the ordinary Dirichlet condition of velocity for some domains of simple geometries, including the two-dimensionalchannel, plane annulus and axisymmetric circular pipe. The Fourier series is employedto obtain the exact solutions formulated by the stream function. While a unique solution exists for most cases, it is found that yet occurs the cases of no solution under acertain slip length and infinitely multiple solutions under an infinitely discrete set ofslip lengths, respectively.