Knots and links in steady solutions of the Euler equation

Details Knots and links in steady solutions of the Euler equation Knots and links in steady solutions of the Euler equation

2010-03-16

arxiv.org/abs/1003.3122v2

Physics

Mathematical Physics

19 pages, 1 figure; Ann. of Math. 174 (2011)

Scientific paper

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.

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