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Knots and links in steady solutions of the Euler equation. (English) Zbl 1238.35092
The incompressible Euler equation describes the motion of the ideal fluid. A steady solution of the Euler equation is given by a Beltrami field, which satisfies the equation \(\text{curl} \, u = \lambda u\). The main theorem says that an arbitrary locally finite link in the space is a set of a stream lines (or a vortex lines) of a Beltrami field. This means that the given link is a periodic orbit of a Beltrami field in a tubular neighborhood of the link.

MSC:
35Q31 Euler equations
37C27 Periodic orbits of vector fields and flows
76B47 Vortex flows for incompressible inviscid fluids
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