Shear Flows of an Ideal Fluid and Elliptic Equations in Unbounded Domains
François Hamel, Nikolai Nadirashvili
Source 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 .© 2016 Wiley Periodicals, Inc.
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