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arXiv · 1904.12495

Associated Weber-Orr transform, Biot-Savart Law and explicit solution of 2D Stokes system in exterior of the disc

A. V. Gorshkov
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Abstract

In this article we derive the explicit solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity $\mathbf{v}_\infty$ at infinity. It turned out it is the first application of the associated Weber-Orr transform to mathematical physics in comparison to classical Weber-Orr transform which is used in many researches. From no-slip condition for velocity field we will obtain Robin-type boundary condition for vorticity. Then the initial-boundary value problem for vorticity will be solved with help of the associated Weber-Orr transform. Also the explicit formula of Biot-Savart Law in polar coordinates will be given.

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A. V. Gorshkov. 2019-04-29. Associated Weber-Orr transform, Biot-Savart Law and explicit solution of 2D Stokes system in exterior of the disc. https://doi.org/10.1007/s00021-019-0445-2

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