Navier-Stokes solutions with point vortex initial data in the half-plane converge to the Lamb-Oseen vortex away from the boundary and to the Prandtl boundary-layer system near the boundary in the zero-viscosity limit.
Maekawa,Spectral Properties of the Linearization at the Burgers Vortex in the High Rotation Limit, J
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The Navier-Stokes equations in $\mathbb R^2_+$ with point vortex initial data: Zero-viscosity limit
Navier-Stokes solutions with point vortex initial data in the half-plane converge to the Lamb-Oseen vortex away from the boundary and to the Prandtl boundary-layer system near the boundary in the zero-viscosity limit.