A Uniqueness Theorem for Incompressible Fluid Flows with Straight Streamlines
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.
 Publication:

Journal of Mathematical Fluid Mechanics
 Pub Date:
 August 2022
 DOI:
 10.1007/s0002102200725z
 arXiv:
 arXiv:2201.02862
 Bibcode:
 2022JMFM...24...90G
 Keywords:

 Euler equations;
 Incompressible fluid;
 Line congruence;
 Mathematics  Analysis of PDEs;
 Mathematical Physics;
 Mathematics  Differential Geometry
 EPrint:
 11 pages LATEX, Separate Appendix document contains REDUCE computer algebra code for the calculations