Journal
COMMUNICATIONS ON PURE AND APPLIED MATHEMATICS
Volume 70, Issue 3, Pages 590-608Publisher
WILEY
DOI: 10.1002/cpa.21670
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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. (C) 2016 Wiley Periodicals, Inc.
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