# 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} }

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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