# A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines

```@article{Guilfoyle2022AUT,
title={A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines},
author={Brendan Guilfoyle},
journal={Journal of Mathematical Fluid Mechanics},
year={2022},
volume={24},
pages={1-11}
}```
• B. Guilfoyle
• Published 8 January 2022
• Mathematics
• Journal of Mathematical Fluid Mechanics
It is proven that the only incompressible Euler fluid flows with fixed straight streamlines are those generated by the normal lines to a round sphere, a circular cylinder or a flat plane, the fluid flow being that of a point source, a line source or a plane source at infinity, respectively. The proof uses the local differential geometry of oriented line congruences to integrate the Euler equations explicitly.

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