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arXiv · 2312.02571

Potential flows away from stagnation in infinite cylinders

François Hamel·Aram Karakhanyan
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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.

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François Hamel, Aram Karakhanyan. 2023-12-05. Potential flows away from stagnation in infinite cylinders. https://arxiv.org/abs/2312.02571

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