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→∞.
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Original Russian Text © V.V. Pukhnachev.
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Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 55, No. 2, pp. 180–187, March–April, 2014.
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Pukhnachev, V.V. Point vortex in a viscous incompressible fluid. J Appl Mech Tech Phy 55, 345–351 (2014). https://doi.org/10.1134/S0021894414020175
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DOI: https://doi.org/10.1134/S0021894414020175