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

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• 作者：Franç ; ois Hamel and Nikolai Nadirashvili
• 刊名：Communications on Pure and Applied Mathematics
• 出版年：2017
• 出版时间：March 2017
• 年：2017
• 卷：70
• 期：3
• 页码：590-608
• 全文大小：230K
• ISSN：1097-0312

文摘

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.