Point vortex in a viscous incompressible fluid

Abstract

A plane steady problem of a point vortex in a domain filled by a viscous incompressible fluid and bounded by a solid wall is considered. The existence of the solution of Navier-Stokes equations, which describe such a flow, is proved in the case where the vortex circulation Θ and viscosity ν satisfy the condition |Θ| < 2πν. The velocity field of the resultant solution has an infinite Dirichlet integral. It is shown that this solution can be approximated by the solution of the problem of rotation of a disk of radius Γ with an angular velocity ω under the condition 2πγ 2 ω → Γ as γ → 0 and ω→∞.