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arXiv · 1509.04463

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

François Hamel·Nikolai Nadirashvili
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Abstract

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

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François Hamel, Nikolai Nadirashvili. 2015-09-15. Shear flows of an ideal fluid and elliptic equations in unbounded domains. https://arxiv.org/abs/1509.04463

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