Shear flows of an ideal fluid and elliptic equations in unbounded\n domains

2015/09/15 by François Hamel, Nikolaï Nadirashvili, Hamel, François +1 · 5 citations
Computer Science · Mathematics · #Advanced Mathematical Modeling in Engineering #Analysis of PDEs (math.AP) #FOS: Mathematics #Geometric Analysis and Curvature Flows #Nonlinear Partial Differential Equations

paper · pdf · doi:10.48550/arxiv.1509.04463

openalex publication_date 2015/09/15 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

We prove that, in a two-dimensional strip, a steady flow of an ideal\nincompressible fluid with no stationary point and tangential boundary\nconditions is a shear flow. The same conclusion holds for a bounded steady flow\nin a half-plane. The proofs are based on the study of the geometric properties\nof the streamlines of the flow and on one-dimensional symmetry results for\nsolutions of some semilinear elliptic equations. Some related rigidity results\nof independent interest are also shown in n-dimensional slabs in any dimension\nn.\n

Cited by

• Dynamics of Ideal Fluid Flows
• Circular flows for the Euler equations in two-dimensional annular domains
• Potential flows away from stagnation in infinite cylinders
• Least total curvature solutions to steady Euler system and monotone solutions to semilinear equations in a strip
• Large-amplitude periodic solutions to the steady Euler equations with piecewise constant vorticity

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