Knots and links in steady solutions of the Euler equation

Abstract

Given any possibly unbounded, locally finite link, we show that there exists a smooth diffeomorphism transforming this link into a set of stream (or vortex) lines of a vector field that solves the steady incompressible Euler equation in $\mathbb{R}^3$. Furthermore, the diffeomorphism can be chosen arbitrarily close to the identity in any $C^r$ norm.

Authors

Alberto Enciso

Instituto de Ciencias Matemáticas
CSIC-UAM-UC3M-UCM
C/ Serrano 123
28006 Madrid
Spain

Daniel Peralta-Salas

Instituto de Ciencias Matemáticas
CSIC-UAM-UC3M-UCM
C/ Serrano 123
28006 Madrid
Spain