Shear flows of an ideal fluid and elliptic equations in unbounded domains
Analysis of PDEs
2015-09-16 v1
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.
Keywords
Cite
@article{arxiv.1509.04463,
title = {Shear flows of an ideal fluid and elliptic equations in unbounded domains},
author = {François Hamel and Nikolai Nadirashvili},
journal= {arXiv preprint arXiv:1509.04463},
year = {2015}
}