Associated Weber–Orr Transform, Biot–Savart Law and Explicit Form of the Solution of 2D Stokes System in Exterior of the DiscстатьяИсследовательская статья
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Дата последнего поиска статьи во внешних источниках: 8 декабря 2019 г.
Аннотация:In this article we derive the explicit formula for the solution of 2-D Stokes system in exterior of the disc with no-slip condition on inner boundary and given velocity {\$}{\$}{\backslash}mathbf {\{}v{\}}{\_}{\backslash}infty {\$}{\$}v∞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.