A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines
Analysis of PDEs
2022-08-02 v1 Mathematical Physics
Differential Geometry
math.MP
Abstract
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.
Cite
@article{arxiv.2201.02862,
title = {A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines},
author = {Brendan Guilfoyle},
journal= {arXiv preprint arXiv:2201.02862},
year = {2022}
}
Comments
11 pages LATEX, Separate Appendix document contains REDUCE computer algebra code for the calculations