Existence of the solution to stationary Navier–Stokes equations with nonlinear slip boundary conditions

The stationary Navier–Stokes equations with nonlinear slip boundary conditions are investigated in this paper. Because the boundary conditions include the subdifferential property on the part boundary, the variational formulation of this problem is the variational inequality problem of the second kind with Navier–Stokes operator. The main purpose of the paper is to study the existence of the weak solution and the strong solution to this variational inequality problem in terms of the Yosidaʼs regularity method.