Abstract: We first prove the existence and uniqueness of solution of quasilinear Stokes equations. Then it is shown when the viscosity vanishes, the solution of the quasilinear Stokes equations tends to the solution of the degenerate equations, in which the viscous term is omitted from the quasilinear Stokes equations and the boundary condition is weakened. In the end, we obtain the boundary layer estimation. Our result shows that the thickness of the boundary layer is proportional to ε^(1)/4.

Key words: Quasilinear Stokes equations, degenerate equations, boundary layer