Example of zero viscosity limit for two-dimensional nonstationary Navier- Stokes flows with boundary. (English) Zbl 0797.76011

Matsui, Shin’ya

Japan J. Ind. Appl. Math. 11, No. 1, 155-170 (1994).

Summary: We construct a Navier-Stokes flow in the unit disk, whose initial data have radially symmetric vorticity. Our goal is to show that this flow is convergent to some Euler flow as the viscosity tends to zero in \(L^ 2\) norm. We give necessary and sufficient conditions for this convergence in \(C([0,T];L^ 2(\Omega))\), where \(\Omega\) is a two-dimensional bounded domain with smooth boundary.

MSC:

76D05	Navier-Stokes equations for incompressible viscous fluids
35Q30	Navier-Stokes equations

Keywords:

boundary layer; unit disk; initial data; radially symmetric vorticity; Euler flow

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