On the zero-viscosity limit of the Navier-Stokes equations in the half-space

Abstract

We consider the zero viscosity limit of the incompressible Navier-Stokes equations with non-slip boundary condition in the half-space for the initial vorticity located away from the boundary. By using the vorticity formulation and Cauchy-Kowaleskaya theorem, Maekawa proved the local in time convergence of the Navier-Stokes equations in the half- plane to the Euler equations outside a boundary layer and to the Prandtl equations in the boundary layer. In this paper, we develop the direct energy method to generalize Maekawa's result to the half-space.

arXiv comment52 pages

References in corpus (1)

• On the ill-posedness of the Prandtl equation

Cited by in corpus (5)

• On the Euler+Prandtl expansion for the Navier-Stokes equations
• Well-posedness in Gevrey function space for 3D Prandtl equations without Structural Assumption
• The inviscid limit for the Navier-Stokes equations with data analytic only near the boundary
• The 3D inviscid limit problem with data analytic near the boundary
• Real analytic local well-posedness for the Triple Deck