Potential flows away from stagnation in infinite cylinders

2023/12/05 by François Hamel, Hamel, François, Aram Karakhanyan +1 · 1 citation
Computer Science · Engineering · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Navier-Stokes equation solutions #Stability and Controllability of Differential Equations

paper · pdf · doi:10.48550/arxiv.2312.02571

openalex publication_date 2023/12/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

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.

Citations

• Liouville theorems for the Navier–Stokes equations and applications
• Partial analyticity and nodal sets for nonlinear elliptic systems
• Shear flows of an ideal fluid and elliptic equations in unbounded\n domains

Cited by

• Rigidity results for finite energy solutions to the stationary 2D Euler equations

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