The Inviscid Limit for the Steady Incompressible Navier-Stokes Equations in the Three Dimension

In this paper, the authors consider the zero-viscosity limit of the three dimensional incompressible steady Navier-Stokes equations in a half space ℝ+ × ℝ2. The result shows that the solution of three dimensional incompressible steady Navier-Stokes equations converges to the solution of three dimensional incompressible steady Euler equations in Sobolev space as the viscosity coefficient going to zero. The method is based on a new weighted energy estimates and Nash-Moser iteration scheme.