Knots and links in steady solutions of the Euler equation

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.