A Liouville theorem for the Euler equations in the plane
Abstract
This paper is concerned with qualitative properties of bounded steady flows of an ideal incompressible fluid with no stagnation point in the twodimensional plane R^2. We show that any such flow is a shear flow, that is, it is parallel to some constant vector. The proof of this Liouvilletype result is firstly based on the study of the geometric properties of the level curves of the stream function and secondly on the derivation of some estimates on the at most logarithmic growth of the argument of the flow. These estimates lead to the conclusion that the streamlines of the flow are all parallel lines.
 Publication:

arXiv eprints
 Pub Date:
 March 2017
 DOI:
 10.48550/arXiv.1703.07293
 arXiv:
 arXiv:1703.07293
 Bibcode:
 2017arXiv170307293H
 Keywords:

 Mathematics  Analysis of PDEs