Potential flows away from stagnation in infinite cylinders
Analysis of PDEs
2025-02-25 v2
Abstract
Steady incompressible potential flows of an inviscid or viscous fluid are considered in infinite N-dimensional cylinders with tangential boundary conditions. We show that such flows, if away from stagnation, are constant and parallel to the direction of the cylinder. This means equivalently that a harmonic function whose gradient is bounded away from zero in an infinite cylinder with Neumann boundary conditions is an affine function. The proof of this rigidity result uses a combination of ODE and PDE arguments, respectively for the streamlines of the flow and the harmonic potential function.
Cite
@article{arxiv.2312.02571,
title = {Potential flows away from stagnation in infinite cylinders},
author = {François Hamel and Aram Karakhanyan},
journal= {arXiv preprint arXiv:2312.02571},
year = {2025}
}