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

Mingwen Fei; Tao Tao; Zhifei Zhang

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arXiv · 1609.03778

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

Mingwen Fei·Tao Tao·Zhifei Zhang

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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.

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Mingwen Fei, Tao Tao, Zhifei Zhang. 2016-09-13. On the zero-viscosity limit of the Navier-Stokes equations in the half-space. https://arxiv.org/abs/1609.03778

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