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

## TL;DR

This paper derives an explicit solution for the 2D Stokes system outside a disc using the novel associated Weber-Orr transform, providing new analytical tools and explicit formulas relevant to fluid dynamics in mathematical physics.

## Contribution

It introduces the first application of the associated Weber-Orr transform to solve the 2D Stokes system in an exterior domain, deriving explicit solutions and formulas.

## Key findings

- Explicit solution of 2D Stokes system outside a disc.
- Derivation of Robin-type boundary condition for vorticity.
- Explicit Biot-Savart Law formula in polar coordinates.

## 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.