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

Abstract

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.

Keywords

Navier-Stokes equations / Euler equations / Zero viscosity limit

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