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Article Dans Une Revue Communications on Pure and Applied Mathematics Année : 2017

Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains

Résumé

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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Dates et versions

hal-01199177 , version 1 (15-09-2015)

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François Hamel, Nikolai Nadirashvili. Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains. Communications on Pure and Applied Mathematics, 2017, 70 (3), pp.590 - 608. ⟨10.1002/cpa.21670⟩. ⟨hal-01199177⟩
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